Primal Interior Point Method for Minimization of Generalized Minimax Functions

0347293 - ÚI 2011 RIV CZ eng J - Journal Article
Lukšan, Ladislav - Matonoha, Ctirad - Vlček, Jan
Primal Interior Point Method for Minimization of Generalized Minimax Functions.
Kybernetika. Roč. 46, č. 4 (2010), s. 697-721. ISSN 0023-5954
R&D Projects: GA ČR GA201/09/1957
Institutional research plan: CEZ:AV0Z10300504
Keywords : unconstrained optimization * large-scale optimization * nonsmooth optimization * generalized minimax optimization * interior-point methods * modified Newton methods * variable metric methods * global convergence * computational experiments
Subject RIV: BA - General Mathematics
Impact factor: 0.461, year: 2010
http://dml.cz/handle/10338.dmlcz/140779

In this paper, 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.
Permanent Link: http://hdl.handle.net/11104/0188099