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Discontinuous but Well-Posed Optimization Problems

Published: 01 September 2006 Publication History

Abstract

Using classes of sequentially pseudocontinuous functions, recently introduced by the authors, the aim of the paper is to investigate Tikhonov and parametric well-posedness for optimization problems when the objective functions are not necessarily sequentially lower semicontinuous. Sequential pseudocontinuity is a property more general than sequential semicontinuity and finds motivations in choice theory, since the continuity of preference relations on first countable topological spaces is characterized by the sequential pseudocontinuity of any utility function. Examples show that it is not possible to improve the results with other well-known classes of discontinuous functions.

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  • (2012)Well-Posedness Under Relaxed Semicontinuity for Bilevel Equilibrium and Optimization Problems with Equilibrium ConstraintsJournal of Optimization Theory and Applications10.1007/s10957-011-9963-7153:1(42-59)Online publication date: 1-Apr-2012

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Published In

cover image SIAM Journal on Optimization
SIAM Journal on Optimization  Volume 17, Issue 3
September 2006
322 pages

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 September 2006

Author Tags

  1. Tikhonov well-posedness
  2. minimum problems
  3. parametric minimum problems
  4. parametric well-posedness
  5. sequentially pseudocontinuous functions

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Cited By

View all
  • (2012)Well-Posedness Under Relaxed Semicontinuity for Bilevel Equilibrium and Optimization Problems with Equilibrium ConstraintsJournal of Optimization Theory and Applications10.1007/s10957-011-9963-7153:1(42-59)Online publication date: 1-Apr-2012

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