The semismooth approach for semi-infinite programming under the Reduction Ansatz

Stein, Oliver
Tezel, Aysun
We study convergence of a semismooth Newton method for generalized semi-infinite programming problems with convex lower level problems where, using NCP functions, the upper and lower level Karush-Kuhn-Tucker conditions of the optimization problem are reformulated as a semismooth system of equations. Nonsmoothness is caused by a possible violation of strict complementarity slackness. We show that the standard regularity condition for convergence of the semismooth Newton method is satisfied under natural assumptions for semi-infinite programs. In fact, under the Reduction Ansatz in the lower level and strong stability in the reduced upper level problem this regularity condition is satisfied. In particular, we do not have to assume strict complementary slackness in the upper level. Numerical examples from, among others, design centering and robust optimization illustrate the performance of the method.


A new multiobjective simulated annealing algorithm
Tekinalp, Ozan (Springer Science and Business Media LLC, 2007-09-01)
A new multiobjective simulated annealing algorithm for continuous optimization problems is presented. The algorithm has an adaptive cooling schedule and uses a population of fitness functions to accurately generate the Pareto front. Whenever an improvement with a fitness function is encountered, the trial point is accepted, and the temperature parameters associated with the improving fitness functions are cooled. Beside well known linear fitness functions, special elliptic and ellipsoidal fitness functions,...
Effective optimization with weighted automata on decomposable trees
Ravve, E. V.; Volkovich, Z.; Weber, Gerhard Wilhelm (Informa UK Limited, 2014-01-02)
In this paper, we consider quantitative optimization problems on decomposable discrete systems. We restrict ourselves to labeled trees as the description of the systems and we use weighted automata on them as our computational model. We introduce a new kind of labeled decomposable trees, sum-like weighted labeled trees, and propose a method, which allows us to reduce the solution of an optimization problem, defined in a fragment of Weighted Monadic Second Order Logic, on such a tree to the solution of effec...
An interactive algorithm for multiobjective ranking for underlying linear and quasiconcave value functions
TEZCANER ÖZTÜRK, DİCLEHAN; Köksalan, Mustafa Murat (Wiley, 2019-07-29)
We develop interactive algorithms to find a strict total order for a set of discrete alternatives for two different value functions: linear and quasiconcave. The algorithms first construct a preference matrix and then find a strict total order. Based on the ordering, they select a meaningful pair of alternatives to present the decision maker (DM) for comparison. We employ methods to find all implied preferences of the DM, after he or she makes a preference. Considering all the preferences of the DM, the pre...
The differential quadrature solution of nonlinear reaction-diffusion and wave equations using several time-integration schemes
Meral, Gulnihal; Tezer, Münevver (Wiley, 2011-04-01)
Three different time-integration schemes, namely the finite difference method (FDM) with a relaxation parameter, the least-squares method (LSM) and the finite element method (FEM), are applied to the differential quadrature (DQM) solution of one-dimensional nonlinear reaction-diffusion and wave equations. In the solution procedure, the space derivatives are discretized using DQM, which may also be used without the need of boundary conditions. The aim of the paper is to find computationally more efficient ti...
The DRBEM solution of incompressible MHD flow equations
Bozkaya, Nuray; Tezer, Münevver (Wiley, 2011-12-10)
This paper presents a dual reciprocity boundary element method (DRBEM) formulation coupled with an implicit backward difference time integration scheme for the solution of the incompressible magnetohydrodynamic (MHD) flow equations. The governing equations are the coupled system of Navier-Stokes equations and Maxwell's equations of electromagnetics through Ohm's law. We are concerned with a stream function-vorticity-magnetic induction-current density formulation of the full MHD equations in 2D. The stream f...
Citation Formats
O. Stein and A. Tezel, “The semismooth approach for semi-infinite programming under the Reduction Ansatz,” JOURNAL OF GLOBAL OPTIMIZATION, pp. 245–266, 2008, Accessed: 00, 2020. [Online]. Available: