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Primal interior point method for minimization of generalized minimax functions

Ladislav Luksan(luksan***at***cs.cas.cz)
Ctirad Matonoha(matonoha***at***cs.cas.cz)
Jan Vlcek(vlcek***at***cs.cas.cz)

Abstract: In this report, we propose a primal interior-point method for large sparse generalized minimax optimization. After a short introduction, where the problem is stated, we introduce the basic equations of the Newton method applied to the KKT conditions and propose a primal interior-point method. Next we describe the basic algorithm and give more details concerning its implementation covering numerical differentiation, variable metric updates, and a barrier parameter decrease. Using standard weak assumptions, we prove that this algorithm is globally convergent if a bounded barrier is used. Then, using stronger assumptions, we prove that it is globally convergent also for the logarithmic barrier. Finally, we present results of computational experiments confirming the efficiency of the primal interior point method for special cases of generalized minimax problems.

Keywords: Unconstrained optimization, large-scale optimization, nonsmooth optimization, generalized minimax optimization, interior-point methods, modified Newton methods, variable metric methods, global convergence, computational experiments.

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Unconstrained Optimization )

Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Technical Report V1017-07, Institute of Computer Science, Czech Academy of Sciences, Prague, December 2007.

Download: [Postscript][PDF]

Entry Submitted: 01/12/2008
Entry Accepted: 01/12/2008
Entry Last Modified: 01/12/2008

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