An Unconstrained Convex Programming Approach to Linear Semi-Infinite Programming

In this paper, an unconstrained convex programming dual approach for solving a class of linear semi-infinite programming problems is proposed. Both primal and dual convergence results are established under some basic assumptions. Numerical examples are also included to illustrate this approach.

[1]  Kenneth O. Kortanek,et al.  Semi-Infinite Programming: Theory, Methods, and Applications , 1993, SIAM Rev..

[2]  Jorge Nocedal,et al.  Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization , 1997, TOMS.

[3]  T. Pietrzykowski The potential method for conditional maxima in the locally compact metric spaces , 1970 .

[4]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[5]  Klaus Glashoff,et al.  Linear Optimization and Approximation , 1983 .

[6]  Werner Krabs,et al.  Optimization and approximation , 1979 .

[7]  The Math Works, Inc. The Math Works Inc , 1991, International Conference on Advances in System Simulation.

[8]  Shu-Cherng Fang,et al.  Linear Optimization and Extensions: Theory and Algorithms , 1993 .

[9]  Nicholas I. M. Gould,et al.  An exact penalty function for semi-infinite programming , 1987, Math. Program..

[10]  丸山 徹 Convex Analysisの二,三の進展について , 1977 .

[11]  S. Fang,et al.  An inexact approach to solving linear semi-infinite programming problems , 1994 .

[12]  Shu-Cherng Fang,et al.  On the entropic perturbation and exponential penalty methods for linear programming , 1996 .

[13]  A. Fiacco,et al.  Survey of penalty, exact-penalty and multiplier methods from 1968 to 1993 ∗ , 1995 .

[14]  Jonathan M. Borwein,et al.  Convergence of Best Entropy Estimates , 1991, SIAM J. Optim..

[15]  F. J. Gould,et al.  An Existence Theorem for Penalty Function Theory , 1974 .

[16]  J. Borwein,et al.  A Survey of Convergence Results for Maximum Entropy Methods , 1993 .

[17]  Chih-Jen Lin,et al.  A Dual Affine Scaling Based Algorithm for Solving Linear Semi-Infinite Programming Problems , 1994 .

[18]  G. Alistair Watson,et al.  A projected lagrangian algorithm for semi-infinite programming , 1985, Math. Program..

[19]  Sven-Åke Gustafson,et al.  On the Computational Solution of a Class of Generalized Moment Problems , 1970 .

[20]  Shu-Cherng Fang,et al.  Linear programming with entropic perturbation , 1993, ZOR Methods Model. Oper. Res..

[21]  Jonathan M. Borwein,et al.  Partially-Finite Programming in L1 and the Existence of Maximum Entropy Estimates , 1993, SIAM J. Optim..

[22]  Michael C. Ferris,et al.  An interior point algorithm for semi-infinite linear programming , 1989, Math. Program..