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New duality results for evenly convex optimization problems.

M D Fajardo1, S M Grad2, J Vidal3

  • 1University of Alicante, Alicante, Spain.

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Summary
This summary is machine-generated.

This study introduces a new dual problem for optimization using even convex functions and Rockafellar

Keywords:
26B2549N1552A2090C25Evenly convex functionLagrangian functionconverse dualityconvex optimization in locally convex spacesgeneralized convex conjugationtotal duality

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Area of Science:

  • Optimization Theory
  • Convex Analysis
  • Functional Analysis

Background:

  • Optimization problems are fundamental in various scientific disciplines.
  • Even convex functions present unique properties within convex analysis.
  • Rockafellar's perturbation theory offers a framework for duality in optimization.

Purpose of the Study:

  • To develop an alternative dual problem for general optimization.
  • To investigate duality conditions using even convexity and c-subdifferentials.
  • To provide formulae for c-subdifferentials and biconjugates in optimization.

Main Methods:

  • Generalized conjugation scheme
  • Rockafellar's perturbation theory
  • c-subdifferentials
  • Saddle-point theory

Main Results:

  • An alternative dual problem for optimization on locally convex spaces.
  • Sufficient conditions for converse and total duality.
  • Formulae for c-subdifferential and biconjugate of objective functions.
  • Characterization of total duality via Lagrangian saddle-points.

Conclusions:

  • The proposed framework extends duality theory for even convex optimization.
  • The results offer new tools for analyzing and solving optimization problems.
  • The study bridges concepts from convex analysis and optimization theory.