Linear semi-infinite programming theory: An updated survey

Solving a class of fuzzy linear programs by using semi-infinite programming techniques☆

SIPAMPL is an environment for coding semi-infinite programming (SIP) problems. This environment includes a database containing a set of SIP problems that have been collected from the literature and a set of routines. It allows users to code their own SIP problems in AMPL, to use any problem already in the database, and to develop and test any SIP solver. The SIPAMPL routines support the interface between a potential SIP solver and test problems coded in AMPL. SIPAMPL also provides a tool that allows the selection of problems from the database with specified characteristics. As a concept demonstration, we show how MATLAB can use SIPAMPL to solve the problems in the database. The Linux and Microsoft Windows versions together with the database of coded problems are freely available via the web.

SIPAMPL: Semi-infinite programming with AMPL

On the numerical treatment of linearly constrained semi-infinite optimization problems

We describe a reduction algorithm for solving semi-infinite programming problems. The proposed algorithm uses the simulated annealing method equipped with a function stretching as a multi-local procedure, and a penalty technique for the finite optimization process. An exponential penalty merit function is reduced along each search direction to ensure convergence from any starting point. Our preliminary numerical results seem to show that the algorithm is very promising in practice. †This paper has been presented at the 8th International Conference on Parametric Optimization and Related Topics (Cairo, Egypt, November–December 2005).

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A reduction method for semi-infinite programming by means of a global stochastic approach

The development of efficient algorithms that provide all the local minima of a function is crucial to solve certain subproblems in many optimization methods. A “multi-local” optimization procedure using inexact line searches is presented, and numerical experiments are also reported. An application of the method to a semi-infinite programming procedure is included.

Susana Sanmatías

Papers

A multi-local optimization algorithm