Comparative study of RPSALG algorithm for convex semi-infinite programming. The Remez penalty and smoothing algorithm (RPSALG) is a unified framework for penalty and smoothing methods for solving min-max convex semi-infinite programing problems, whose convergence was analyzed in a previous paper of three of the authors. In this paper we consider a partial implementation of RPSALG for solving ordinary convex semi-infinite programming problems. Each iteration of RPSALG involves two types of auxiliary optimization problems: the first one consists of obtaining an approximate solution of some discretized convex problem, while the second one requires to solve a non-convex optimization problem involving the parametric constraints as objective function with the parameter as variable. In this paper we tackle the latter problem with a variant of the cutting angle method called ECAM, a global optimization procedure for solving Lipschitz programming problems. We implement different variants of RPSALG which are compared with the unique publicly available SIP solver, NSIPS, on a battery of test problems.
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References in zbMATH (referenced in 2 articles , 1 standard article )
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- Auslender, A.; Ferrer, A.; Goberna, M.A.; López, M.A.: Comparative study of RPSALG algorithm for convex semi-infinite programming (2015)
- Goberna, Miguel A.; López, Marco A.: Post-optimal analysis in linear semi-infinite optimization (2014)