Encyclopedia of Optimization (Springer Reference)

Cover Page......Page 1 Encyclopedia of Optimization......Page 2 Preface to the Second Edition......Page 5 About the Editors......Page 6 Editorial Board Members......Page 8 List of Contributors......Page 10 ABS Algorithms for Linear Equations and Linear Least Squares......Page 33 ABS Algorithms for Optimization......Page 39 Adaptive Convexification in Semi-Infinite Optimization......Page 46 Adaptive Global Search......Page 51 Adaptive Simulated Annealing and its Application to Protein Folding......Page 53 Airline Optimization......Page 58 Algorithmic Improvements Using a Heuristic Parameter, Reject Index for Interval Optimization......Page 62 Algorithms for Genomic Analysis......Page 65 Alignment Problem......Page 86 αBB Algorithm......Page 93 Alternative Set Theory......Page 105 Approximation of Extremum Problems with Probability Functionals......Page 110 Approximation ofMultivariate Probability Integrals......Page 115 Approximations to Robust Conic Optimization Problems......Page 122 Archimedes and the Foundations of Industrial Engineering......Page 128 Asset Liability Management Decision Support System......Page 130 Assignment and Matching......Page 138 Assignment Methods in Clustering......Page 140 Asymptotic Properties of Random Multidimensional Assignment Problem......Page 146 Asynchronous Distributed Optimization Algorithms......Page 155 Auction Algorithms......Page 160 Automatic Differentiation: Calculation of the Hessian......Page 165 Automatic Differentiation: Calculation of Newton Steps......Page 169 Automatic Differentiation: Geometry of Satellites and Tracking Stations......Page 174 Automatic Differentiation: Introduction, History and Rounding Error Estimation......Page 185 Automatic Differentiation: Parallel Computation......Page 191 Automatic Differentiation: Point and Interval......Page 197 Automatic Differentiation: Point and Interval Taylor Operators......Page 203 Automatic Differentiation: Root Problemand Branch Problem......Page 208 Bayesian Global Optimization......Page 214 Bayesian Networks......Page 218 Beam Selection in Radiotherapy Treatment Design......Page 227 Best Approximation in Ordered Normed Linear Spaces......Page 233 Bilevel Fractional Programming......Page 250 Bilevel Linear Programming......Page 252 Bilevel Linear Programming: Complexity, Equivalence to Minmax, Concave Programs......Page 256 Bilevel Optimization: Feasibility Test and Flexibility Index......Page 259 Bilevel Programming......Page 270 Bilevel Programming: Applications......Page 272 Bilevel Programming: Applications in Engineering......Page 274 Bilevel Programming Framework for Enterprise-Wide Process Networks Under Uncertainty......Page 279 Bilevel Programming: Global Optimization......Page 286 Bilevel Programming: Implicit Function Approach......Page 291 Bilevel Programming: Introduction, History and Overview......Page 297 Bilevel Programming in Management......Page 300 Bilevel Programming: Optimality Conditions and Duality......Page 305 Bilinear Programming......Page 310 Bilinear Programming: Applications in the Supply Chain Management......Page 313 Bi-Objective Assignment Problem......Page 319 Biquadratic Assignment Problem......Page 324 Bisection Global Optimization Methods......Page 325 Boolean and Fuzzy Relations......Page 328 Bottleneck Steiner Tree Problems......Page 342 Boundary Condition Iteration BCI......Page 344 Bounding Derivative Ranges......Page 349 Bounds and Solution Vector Estimates for Parametric NLPS......Page 356 Branch and Price: Integer Programming with Column Generation......Page 359 Branchwidth and Branch Decompositions1......Page 363 Broadcast Scheduling Problem......Page 370 Broyden Family ofMethods and the BFGS Update......Page 376 CapacitatedMinimum Spanning Trees......Page 378 Carathéodory, Constantine......Page 388 Carathéodory Theorem......Page 389 Checklist Paradigm Semantics for Fuzzy Logics......Page 390 Chemical Process Planning......Page 400 Cholesky Factorization......Page 405 CombinatorialMatrix Analysis......Page 408 Combinatorial Optimization Algorithms in Resource Allocation Problems......Page 413 Combinatorial Optimization Games......Page 418 Combinatorial Test Problems and Problem Generators......Page 422 Communication Network Assignment Problem......Page 425 Competitive Facility Location......Page 427 Competitive Ratio for Portfolio Management......Page 432 Complementarity Algorithms in Pattern Recognition......Page 436 Complexity Classes in Optimization......Page 444 Complexity of Degeneracy......Page 450 Complexity of Gradients, Jacobians, and Hessians......Page 456 Complexity and Large-Scale Least Squares Problems......Page 466 Complexity Theory......Page 478 Complexity Theory: Quadratic Programming......Page 482 Composite Nonsmooth Optimization......Page 485 Computational Complexity Theory......Page 488 Concave Programming......Page 493 Conjugate-Gradient Methods......Page 497 ContactMap OverlapMaximization Problem, CMO......Page 502 Continuous Approximations to Subdifferentials......Page 506 Continuous Global Optimization: Applications......Page 513 Continuous Global Optimization: Models, Algorithms and Software......Page 517 Continuous Reformulations of Discrete-Continuous Optimization Problems......Page 524 Continuous Review Inventory Models: (Q, R) Policy......Page 532 Contraction-Mapping......Page 536 Control Vector Iteration CVI......Page 540 Convex Discrete Optimization......Page 544 Convex Envelopes in Optimization Problems......Page 581 Convexifiable Functions, Characterization of1......Page 582 Convex Max-Functions......Page 586 Convex-Simplex Algorithm......Page 589 Copositive Optimization......Page 592 Copositive Programming......Page 595 Cost Approximation Algorithms......Page 598 Credit Rating and OptimizationMethods......Page 609 Criss-Cross Pivoting Rules......Page 615 Cutting PlaneMethods for Global Optimization......Page 621 Cutting-Stock Problem......Page 625 Cyclic Coordinate Method......Page 626 Data Envelopment Analysis......Page 628 Data Mining......Page 631 D.C. Programming......Page 638 Decision Support Systems withMultiple Criteria......Page 643 Decomposition Algorithms for the Solution of Multistage Mean-Variance Optimization Problems......Page 650 Decomposition in Global Optimization......Page 658 Decomposition Principle of Linear Programming......Page 661 Decomposition Techniques forMILP: Lagrangian Relaxation......Page 663 De Novo Protein Design Using Flexible Templates......Page 669 De Novo Protein Design Using Rigid Templates......Page 674 Derivative-Free Methods for Non-smooth Optimization......Page 679 Derivatives of Markov Processes and Their Simulation......Page 686 Derivatives of Probability and Integral Functions: General Theory and Examples......Page 689 Derivatives of Probability Measures......Page 695 Design Optimization in Computational Fluid Dynamics......Page 697 Design of Robust Model-Based Controllers via Parametric Programming......Page 708 Determining the Optimal Number of Clusters......Page 718 Deterministic and Probabilistic OptimizationModels for Data Classification......Page 725 Differential Equations and Global Optimization......Page 733 Dini and Hadamard Derivatives in Optimization......Page 741 Directed Tree Networks......Page 747 Direct Global Optimization Algorithm......Page 756 Direct Search Luus–Jaakola Optimization Procedure......Page 766 Discontinuous Optimization......Page 770 Discretely Distributed Stochastic Programs: Descent Directions and Efficient Points......Page 775 Discrete Stochastic Optimization......Page 782 Disease Diagnosis: Optimization-BasedMethods......Page 784 Disjunctive Programming......Page 815 Distance Dependent Protein Force Field via Linear Optimization......Page 818 Domination Analysis in Combinatorial Optimization......Page 823 Duality Gaps in Nonconvex Optimization......Page 833 Duality in Optimal Control with First Order Differential Equations......Page 836 Duality for Semidefinite Programming......Page 842 Duality Theory: Biduality in Nonconvex Optimization......Page 845 Duality Theory: Monoduality in Convex Optimization......Page 849 Duality Theory: Triduality in Global Optimization......Page 853 Dykstra’s Algorithm and Robust Stopping Criteria......Page 859 Dynamic Programming: Average Cost Per Stage Problems......Page 864 Dynamic Programming in Clustering......Page 868 Dynamic Programming: Continuous-time Optimal Control......Page 875 Dynamic Programming: Discounted Problems......Page 877 Dynamic Programming: Infinite Horizon Problems, Overview......Page 881 Dynamic Programming: Inventory Control......Page 884 Dynamic Programming and Newton’sMethod in Unconstrained Optimal Control......Page 887 Dynamic Programming: Optimal Control Applications......Page 893 Dynamic Programming: Stochastic Shortest Path Problems......Page 900 Dynamic Programming: Undiscounted Problems......Page 904 Dynamic Traffic Networks......Page 907 Economic Lot-Sizing Problem......Page 914 Eigenvalue Enclosures for Ordinary Differential Equations......Page 918 Ellipsoid Method......Page 921 Emergency Evacuation, OptimizationModeling......Page 931 Entropy Optimization: Interior PointMethods......Page 938 Entropy Optimization: Parameter Estimation......Page 943 Entropy Optimization: ShannonMeasure of Entropy and its Properties......Page 947 Equality-Constrained Nonlinear Programming: KKT Necessary Optimality Conditions......Page 952 Equilibrium Networks......Page 954 Equivalence Between Nonlinear Complementarity Problem and Fixed Point Problem......Page 958 Estimating Data for Multicriteria Decision Making Problems: Optimization Techniques......Page 962 Evacuation Networks......Page 971 Evolutionary Algorithms in Combinatorial Optimization......Page 981 Extended Cutting Plane Algorithm......Page 990 Extension of the Fundamental Theorem of Linear Programming......Page 997 Extremum Problems with Probability Functions: Kernel Type Solution Methods......Page 1000 Facilities Layout Problems......Page 1005 Facility Location with Externalities......Page 1009 Facility Location Problems with Spatial Interaction......Page 1012 Facility Location with Staircase Costs......Page 1019 Farkas Lemma......Page 1025 Farkas Lemma: Generalizations......Page 1028 Feasible Sequential Quadratic Programming......Page 1031 Feedback Set Problems......Page 1035 Fejér Monotonicity in Convex Optimization......Page 1046 Financial Applications of Multicriteria Analysis......Page 1054 Financial Equilibrium......Page 1065 Financial Optimization......Page 1070 Finite Complete Systems of Many-valued Logic Algebras......Page 1078 First Order Constraint Qualifications......Page 1085 Flow Shop Scheduling Problem......Page 1090 Forecasting......Page 1098 Fourier–Motzkin Elimination Method......Page 1104 Fractional Combinatorial Optimization......Page 1107 Fractional Programming......Page 1110 Fractional Zero-One Programming......Page 1121 Frank–Wolfe Algorithm......Page 1124 Frequency Assignment Problem......Page 1127 Fundamental Theorem of Algebra......Page 1131 FuzzyMulti-objective Linear Programming......Page 1133 Gasoline Blending and Distribution Scheduling: AnMILPModel......Page 1143 Gauss, Carl Friedrich......Page 1157 Gauss–Newton Method: Least Squares, Relation to Newton’s Method......Page 1159 Gene Clustering: A Novel Decomposition-Based Clustering Approach: Global Optimum Search with Enhanced Positioning......Page 1164 Generalizations of Interior Point Methods for the Linear Complementarity Problem......Page 1175 Generalized Assignment Problem......Page 1183 Generalized Benders Decomposition......Page 1192 Generalized Concavity in Multi-objective Optimization......Page 1205 Generalized Disjunctive Programming......Page 1210 Generalized Eigenvalue Proximal Support VectorMachine Problem......Page 1213 Generalized Geometric Programming: Mixed Continuous and Discrete Free Variables......Page 1215 Generalized Monotone MultivaluedMaps......Page 1223 Generalized Monotone Single Valued Maps......Page 1227 Generalized Monotonicity: Applications to Variational Inequalities and Equilibrium Problems......Page 1232 Generalized Networks......Page 1239 Generalized Nonlinear Complementarity Problem......Page 1244 Generalized Outer Approximation......Page 1245 Generalized Primal-relaxed Dual Approach......Page 1253 Generalized Semi-infinite Programming: Optimality Conditions......Page 1257 Generalized Total Least Squares......Page 1263 Generalized Variational Inequalities: A Brief Review......Page 1268 General Moment Optimization Problems......Page 1274 General Routing Problem......Page 1282 Genetic Algorithms......Page 1284 Genetic Algorithms for Protein Structure Prediction......Page 1287 Geometric Programming......Page 1290 Global Equilibrium Search......Page 1298 Globally Convergent Homotopy Methods......Page 1302 Global Optimization Algorithms for Financial Planning Problems......Page 1307 Global Optimization in the Analysis and Management of Environmental Systems......Page 1312 Global Optimization: Application to Phase Equilibrium Problems......Page 1316 Global Optimization Based on StatisticalModels......Page 1321 Global Optimization in Batch Design Under Uncertainty......Page 1324 Global Optimization in Binary Star Astronomy......Page 1329 Global Optimization: Cutting Angle Method......Page 1334 Global Optimization: Envelope Representation......Page 1341 Global Optimization: Filled Function Methods......Page 1346 Global Optimization: Functional Forms......Page 1353 Global Optimization: g- αBB Approach......Page 1358 Global Optimization in Generalized Geometric Programming......Page 1363 Global Optimization of Heat Exchanger Networks......Page 1367 Global Optimization: Hit and RunMethods......Page 1372 Global Optimization: Interval Analysis and Balanced Interval Arithmetic......Page 1376 Global Optimization in Lennard–Jones andMorse Clusters......Page 1380 Global Optimization in Location Problems......Page 1384 Global Optimization Methods for Harmonic Retrieval......Page 1389 Global Optimization Methods for Systems of Nonlinear Equations......Page 1394 Global Optimization in Multiplicative Programming......Page 1396 Global Optimization: p-αBB Approach......Page 1400 Global Optimization in Phase and Chemical Reaction Equilibrium......Page 1406 Global Optimization of Planar Multilayered Dielectric Structures......Page 1413 Global Optimization in Protein Folding......Page 1422 Global Optimization: Tight Convex Underestimators......Page 1441 Global Optimization Using Space Filling......Page 1448 Global Optimization in Weber’s Problem with Attraction and Repulsion......Page 1453 Pairwise Protein Sequence via Mixed-Integer Optimization......Page 1457 Global Supply Chain Models......Page 1464 Global Terrain Methods......Page 1467 Graph Coloring......Page 1474 Graph Planarization......Page 1478 Graph Realization via Semidefinite Programming......Page 1483 Greedy Randomized Adaptive Search Procedures......Page 1490 Gröbner Bases for Polynomial Equations......Page 1499 Hamilton–Jacobi–Bellman Equation......Page 1502 Hemivariational Inequalities: Applications inMechanics......Page 1506 Hemivariational Inequalities: Eigenvalue Problems......Page 1512 Hemivariational Inequalities: Static Problems......Page 1517 Heuristic and Metaheuristic Algorithms for the Traveling Salesman Problem......Page 1528 Heuristic Search......Page 1535 Heuristics for Maximum Clique and Independent Set......Page 1537 High-order Maximum Principle for Abnormal Extremals......Page 1549 High-order Necessary Conditions for Optimality for Abnormal Points......Page 1556 Hilbert’s Thirteenth Problem......Page 1564 History of Optimization......Page 1567 Homogeneous Selfdual Methods for Linear Programming......Page 1571 Hyperplane Arrangements......Page 1574 Hyperplane Arrangements in Optimization......Page 1576 IdentificationMethods for Reaction Kinetics and Transport......Page 1578 Ill-posed Variational Problems......Page 1585 Image Space Approach to Optimization......Page 1590 Implicit Lagrangian......Page 1596 Increasing and Convex-Along-Rays Functions on Topological Vector Spaces......Page 1600 Increasing and Positively Homogeneous Functions on Topological Vector Spaces......Page 1605 Inequality-constrained Nonlinear Optimization......Page 1615 Inference of Monotone Boolean Functions......Page 1620 Infinite Horizon Control and Dynamic Games......Page 1627 Information-based Complexity and Information-based Optimization......Page 1632 Integer Linear Complementary Problem......Page 1637 Integer Linear Programs for Routing and Protection Problems in Optical Networks......Page 1639 Integer Programming......Page 1646 Integer Programming: Algebraic Methods......Page 1653 Integer Programming: Branch and Bound Methods......Page 1663 Integer Programming: Branch and Cut Algorithms......Page 1672 Integer Programming: Cutting Plane Algorithms......Page 1679 Integer Programming Duality......Page 1686 Integer Programming: Lagrangian Relaxation......Page 1696 Integrated Planning and Scheduling......Page 1702 Interior PointMethods for Semidefinite Programming......Page 1708 Interval Analysis: Application to Chemical Engineering Design Problems......Page 1712 Interval Analysis: Differential Equations......Page 1715 Interval Analysis: Eigenvalue Bounds of Interval Matrices......Page 1718 Interval Analysis: Intermediate Terms......Page 1725 Interval Analysis: Nondifferentiable Problems......Page 1728 Interval Analysis for Optimization of Dynamical Systems......Page 1731 Interval Analysis: Parallel Methods for Global Optimization......Page 1738 Interval Analysis: Subdivision Directions in Interval Branch and Bound Methods......Page 1746 Interval Analysis: Systems of Nonlinear Equations......Page 1750 Interval Analysis: Unconstrained and Constrained Optimization......Page 1756 Interval Analysis: Verifying Feasibility......Page 1759 Interval Constraints......Page 1762 Interval Fixed Point Theory......Page 1765 Interval Global Optimization......Page 1768 Interval Linear Systems......Page 1786 Interval Newton Methods......Page 1792 Inventory Management in Supply Chains......Page 1795 Invexity and its Applications......Page 1799 Isotonic Regression Problems......Page 1803 Jaynes’ Maximum Entropy Principle......Page 1807 Job-shop Scheduling Problem......Page 1810 Kantorovich, Leonid Vitalyevich......Page 1817 Kolmogorov Complexity......Page 1818 Kuhn–Tucker Optimality Conditions......Page 1822 Lagrange, Joseph-Louis......Page 1826 Lagrange-Type Functions......Page 1827 Lagrangian Duality: BASICS......Page 1832 Lagrangian Multipliers Methods for Convex Programming......Page 1840 Laplace Method and Applications to Optimization Problems......Page 1845 Large Scale Trust Region Problems......Page 1849 Large Scale Unconstrained Optimization......Page 1858 L-convex Functions andM-convex Functions......Page 1865 LCP: Pardalos–Rosen Mixed Integer Formulation......Page 1872 Least-index Anticycling Rules......Page 1874 Least Squares Orthogonal Polynomials......Page 1878 Least Squares Problems......Page 1883 Leibniz, Gottfried Wilhelm......Page 1893 Lemke Method......Page 1895 Lexicographic Pivoting Rules......Page 1897 Linear Complementarity Problem......Page 1901 Linear Optimization: Theorems of the Alternative......Page 1905 Linear Ordering Problem......Page 1908 Linear Programming......Page 1910 Linear Programming: Interior Point Methods......Page 1913 Linear Programming: Karmarkar Projective Algorithm......Page 1916 Linear Programming: Klee–Minty Examples......Page 1918 Linear Programming Models for Classification......Page 1924 Linear Space......Page 1928 Lipschitzian Operators in Best Approximation by Bounded or Continuous Functions......Page 1929 Load Balancing for Parallel Optimization Techniques......Page 1932 Local Attractors for Gradient-related Descent Iterations......Page 1938 Location Routing Problem......Page 1946 Logconcave Measures, Logconvexity......Page 1952 Logconcavity of Discrete Distributions......Page 1954 Logic-Based Outer Approximation......Page 1955 Lovász Number......Page 1959 LP Strategy for Interval-Newton Method in Deterministic Global Optimization......Page 1964 L-shapedMethod for Two-stage Stochastic Programs with Recourse......Page 1970 Maritime Inventory Routing Problems......Page 1973 Mathematical Programming for DataMining......Page 1981 Mathematical Programming Methods in Supply Chain Management......Page 1985 Matrix Completion Problems......Page 1993 Matroids......Page 2001 Maximum Constraint Satisfaction: Relaxations and Upper Bounds......Page 2007 Maximum Cut Problem, MAX-CUT......Page 2017 Maximum Entropy and Game Theory......Page 2025 Maximum Entropy Principle: Image Reconstruction......Page 2030 Maximum Flow Problem......Page 2035 Maximum Likelihood Detection via Semidefinite Programming......Page 2046 Maximum Partition Matching......Page 2055 Maximum Satisfiability Problem......Page 2061 Medium-Term Scheduling of Batch Processes......Page 2067 Metaheuristic Algorithms for the Vehicle Routing Problem......Page 2081 Metaheuristics......Page 2087 Minimax: Directional Differentiability......Page 2101 Minimax Game Tree Searching......Page 2105 Minimax Theorems......Page 2113 Minimum Concave Transportation Problems......Page 2119 Minimum Cost Flow Problem......Page 2121 MINLP: Application in Facility Location-allocation......Page 2134 MINLP: Applications in Blending and Pooling Problems......Page 2140 MINLP: Applications in the Interaction of Design and Control......Page 2147 MINLP: Branch and Bound Global Optimization Algorithm......Page 2158 MINLP: Branch and Bound Methods......Page 2164 MINLP: Design and Scheduling of Batch Processes......Page 2168 MINLP: Generalized Cross Decomposition......Page 2174 MINLP: Global Optimization with αBB......Page 2181 MINLP: Heat Exchanger Network Synthesis......Page 2189 MINLP: Logic-based Methods......Page 2196 MINLP: Mass and Heat Exchanger Networks......Page 2199 MINLP: Outer Approximation Algorithm......Page 2205 MINLP: Reactive Distillation Column Synthesis......Page 2209 MINLP: Trim-loss Problem......Page 2216 Mixed 0-1 Linear Programming Approach for DNA Transcription Element Identification......Page 2225 Mixed Integer Classification Problems......Page 2236 Mixed Integer Linear Programming: Heat Exchanger Network Synthesis......Page 2240 Mixed Integer Linear Programming: Mass and Heat Exchanger Networks......Page 2243 Mixed Integer Nonlinear Bilevel Programming: Deterministic Global Optimization......Page 2251 Mixed-Integer Nonlinear Optimization: A Disjunctive Cutting Plane Approach......Page 2256 Mixed Integer Nonlinear Programming......Page 2260 Mixed Integer Optimization in Well Scheduling......Page 2273 Mixed Integer Programming/Constraint Programming Hybrid Methods......Page 2296 Model Based Control for Drug Delivery Systems......Page 2302 Modeling Difficult Optimization Problems......Page 2310 Modeling Languages in Optimization: A New Paradigm......Page 2323 Molecular Distance Geometry Problem......Page 2331 Molecular Structure Determination: Convex Global Underestimation......Page 2337 Monotonic Optimization......Page 2342 Monte-Carlo Simulated Annealing in Protein Folding......Page 2349 Monte-Carlo Simulations for Stochastic Optimization......Page 2363 Motzkin Transposition Theorem......Page 2371 Multi-Class Data Classification via Mixed-Integer Optimization......Page 2374 Multicommodity Flow Problems......Page 2380 Multicriteria Decision Support Methodologies for Auditing Decisions......Page 2388 Multicriteria Methods for Mergers and Acquisitions......Page 2398 Multicriteria Sorting Methods......Page 2405 Multidimensional Assignment Problem......Page 2422 Multidimensional Knapsack Problems......Page 2428 Multidisciplinary Design Optimization......Page 2432 Multifacility and Restricted Location Problems......Page 2435 Multi-index Transportation Problems......Page 2439 Multilevel Methods for Optimal Design......Page 2445 Multilevel Optimization in Mechanics......Page 2454 Multi-objective Combinatorial Optimization......Page 2463 Multi-objective Fractional Programming Problems......Page 2468 Multi-objective Integer Linear Programming......Page 2474 Multi-objective Mixed Integer Programming......Page 2480 Multi-objective Optimization and Decision Support Systems......Page 2486 Multi-objective Optimization: Interaction of Design and Control......Page 2491 Multi-objectiveOptimization: InteractiveMethods for Preference Value Functions......Page 2497 Multi-objective Optimization: Lagrange Duality......Page 2500 Multi-objective Optimization: Pareto Optimal Solutions, Properties......Page 2504 Multiparametric Linear Programming......Page 2508 Multiparametric Mixed Integer Linear Programming......Page 2510 Multiple Minima Problem in Protein Folding: αBB Global Optimization Approach......Page 2516 Multiple Objective Dynamic Programming......Page 2523 Multiple Objective Programming Support......Page 2529 Multiplicative Programming......Page 2537 Multi-Quadratic Integer Programming: Models and Applications......Page 2539 Multi-Scale Global Optimization Using Terrain/Funneling Methods......Page 2546 Multistage Stochastic Programming: Barycentric Approximation......Page 2553 Nested Partitions Optimization......Page 2558 Network Design Problems......Page 2564 Network Location: Covering Problems......Page 2570 Neural Networks for Combinatorial Optimization......Page 2572 Neuro-Dynamic Programming......Page 2580 New Hybrid Conjugate Gradient Algorithms for Unconstrained Optimization......Page 2585 Nonconvex Energy Functions: Hemivariational Inequalities......Page 2596 Nonconvex Network Flow Problems......Page 2603 Nonconvex-nonsmooth Calculus of Variations......Page 2606 Nondifferentiable Optimization......Page 2609 Nondifferentiable Optimization: Cutting PlaneMethods......Page 2615 Nondifferentiable Optimization: Minimax Problems......Page 2620 Nondifferentiable Optimization: Newton Method......Page 2627 Nondifferentiable Optimization: Parametric Programming......Page 2632 Nondifferentiable Optimization: Relaxation Methods......Page 2640 Nondifferentiable Optimization: Subgradient Optimization Methods......Page 2643 Nonlinear Least Squares: Newton-type Methods......Page 2644 Nonlinear Least Squares Problems......Page 2651 Nonlinear Least Squares: Trust Region Methods......Page 2655 Nonlinear Systems of Equations: Application to the Enclosure of All Azeotropes......Page 2662 Nonlocal Sensitivity Analysis with Automatic Differentiation......Page 2667 Nonoriented Multicommodity Flow Problems......Page 2672 Nonsmooth Analysis: Fréchet Subdifferentials......Page 2676 Nonsmooth Analysis: Weak Stationarity......Page 2683 Nonsmooth Optimization Approach to Clustering......Page 2690 Nonsmooth and Smoothing Methods for Nonlinear Complementarity Problems and Variational Inequalities......Page 2696 NP-complete Problems and Proof Methodology......Page 2700 Numerical Methods for Unary Optimization......Page 2707 Oligopolistic Market Equilibrium......Page 2715 Operations Research......Page 2718 Operations Research and Financial Markets......Page 2720 Operations Research Models for Supply Chain Management and Design......Page 2728 Optimal Control of a Flexible Arm......Page 2739 Optimal Design of Composite Structures......Page 2742 Optimal Design in Nonlinear Optics......Page 2749 Optimality Criteria for Multiphase Chemical Equilibrium......Page 2755 Optimal Planning of Offshore Oilfield Infrastructure......Page 2762 Optimal Sensor Scheduling......Page 2770 Optimal Solvent Design Approaches......Page 2774 Optimal Triangulations......Page 2781 Optimization in Ad Hoc Networks......Page 2788 Optimization Based Framework for Radiation Therapy......Page 2798 Optimization-Based Visualization......Page 2809 Optimization in Boolean Classification Problems......Page 2815 Optimization in Classifying Text Documents......Page 2820 Optimization and Decision Support Systems......Page 2827 Optimization with Equilibrium Constraints: A Piecewise SQP Approach......Page 2831 Optimization in Leveled Graphs......Page 2837 Optimization in Medical Imaging......Page 2844 Optimization in Operation of Electric and Energy Power Systems......Page 2848 Optimization Problems in Unit-Disk Graphs......Page 2856 Optimization Software......Page 2868 Optimization Strategies for Dynamic Systems......Page 2871 Optimization Techniques for Phase Retrieval Based on Single-Crystal X-Ray Diffraction Data......Page 2882 Optimization in Water Resources......Page 2887 Optimizing Facility Location with Euclidean and Rectilinear Distances......Page 2893 Order Complementarity......Page 2897 Oriented Matroids......Page 2902 Orthogonal Triangularization......Page 2910 Outranking Methods......Page 2911 Overdetermined Systems of Linear Equations......Page 2918 Packet Annealing......Page 2921 Parallel Computing: Complexity Classes......Page 2924 Parallel Computing: Models......Page 2927 Parallel Heuristic Search......Page 2932 Parametric Global Optimization: Sensitivity......Page 2936 Parametric Linear Programming: Cost Simplex Algorithm......Page 2941 Parametric Mixed Integer Nonlinear Optimization......Page 2944 Parametric Optimization: Embeddings, Path Following and Singularities......Page 2948 Peptide Identification via Mixed-Integer Optimization......Page 2954 Performance Profiles of Conjugate-Gradient Algorithms for Unconstrained Optimization......Page 2962 Phase Problem in X-ray Crystallography: Shake and Bake Approach......Page 2977 Piecewise Linear Network Flow Problems......Page 2982 Pivoting Algorithms for Linear Programming Generating Two Paths......Page 2989 Planning in the Process Industry......Page 2994 Plant Layout Problems and Optimization......Page 3003 Pontryagin Maximum Principle......Page 3011 Portfolio Selection: Markowitz Mean-variance Model......Page 3014 Portfolio Selection and Multicriteria Analysis......Page 3020 Potential Reduction Methods for Linear Programming......Page 3032 Powell Method..