Infinite programming : proceedings of an international symposium on Infinite Dimensional Linear Programming, Churchill College, Cambridge, United Kingdom, September 7-10, 1984

Infinite programming may be defined as the study of mathematical programming problems in which the number of variables and the number of constraints are both possibly infinite. Many optimization problems in engineering, operations research, and economics have natural formul- ions as infinite programs. For example, the problem of Chebyshev approximation can be posed as a linear program with an infinite number of constraints. Formally, given continuous functions f, gl, g2," ", gn on the interval [a, b], we can find the linear combination of the functions gl, g2 ..., gn which is the best uniform approximation to f by choosing real numbers a, xl, x2," ., x to n minimize a t€ [a, b]. This is an example of a semi-infinite program; the number of variables is finite and the number of constraints is infinite. An example of an infinite program in which the number of constraints and the number of variables are both infinite, is the well-known continuous linear program which can be formulated as follows. T minimize ~ c(t)Tx(t)dt t b(t), subject to Bx(t) + fo Kx(s)ds x(t) .. 0, t € [0, T] " If x is regarded as a member of some infinite-dimensional vector space of functions, then this problem is a linear program posed over that space. Observe that if the constraint equations are differentiated, then this problem takes the form of a linear optimal control problem with state IV variable inequality constraints Front Matter....Pages N2-XIV Openness, Closedness and Duality in Banach Spaces with Applications to Continuous Linear Programming....Pages 1-15 Conditions for the Closedness of the Characteristic Cone Associated with an Infinite Linear System....Pages 16-28 Symmetric Duality: A Prelude....Pages 29-36 Algebraic fundamentals of linear programming....Pages 37-52 On Regular Semi-Infinite Optimization....Pages 53-64 Semi-Infinite Programming and Continuum Physics....Pages 65-78 On the computation of membrane-eigenvalues by semi-infinite programming methods....Pages 79-89 Lagrangian Methods for Semi-Infinite Programming Problems....Pages 90-107 A New Primal Algorithm for Semi-Infinite Linear Programming....Pages 108-122 Extreme Points and Purification Algorithms in General Linear Programming....Pages 123-135 Network Programming in Continuous Time with Node Storage....Pages 136-153 The Theorem of Gale for Infinite Networks and Applications....Pages 154-171 Nonlinear Optimal Control Problems as Infinite-Dimensional Linear Programming Problems....Pages 172-184 Continuity and Asymptotic Behaviour of the Marginal Function in Optimal Control....Pages 185-193 Alternative Theorems for General Complementarity Problems....Pages 194-203 Nonsmooth Analysis and Optimization for a Class of Nonconvex Mappings....Pages 204-218 Minimum Norm Problems in Normed Vector Lattices....Pages 219-225 “Stochastic Nonsmooth Analysis And Optimization In Banach Spaces”....Pages 226-242 Back Matter....Pages 243-246