Original scientific paper
A NOTE ON LOGARITHMIC SMOOTHING IN SEMI-INFINITE OPTIMIZATION UNDER REDUCTION APPROACH*
Francisco Guerra-Vazquez
; Universidad de las Americas, Puebla, Escuela de Ciencias, San Andres Cholula, Puebla, Mexico
Jan-J. Rückmann
; School of Mathematics, University of Birmingham, Birmingham, United Kingdom
Abstract
This note deals with a semi-infinite optimization problem which is defined by infinitely many inequality constraints. By applying a logarithmic barrier function, a family of interior point approximations of the feasible set is obtained where locally the original feasible set and its
approximations are homeomorphic. Under generic assumptions on the structure of the original feasible set, strongly stable stationary points of the original problem are considered and it is shown that there is
a one-to-one correspondence between the stationary points (and their stationary indices) of the original problem and those of its approximations. Corresponding convergence results, global aspects and a relationship to a standard interior-point approach are discussed.
Keywords
semi-infinite optimization problem; logarithmic smoothing; stationary points
Hrčak ID:
97368
URI
Publication date:
1.2.2013.
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