Characterizations of Solution Sets of Differentiable Quasiconvex Programming Problems View Full Text


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Article Info

DATE

2019-04

AUTHORS

Vsevolod I. Ivanov

ABSTRACT

In this paper, we study some problems with a continuously differentiable and quasiconvex objective function. We prove that exactly one of the following two alternatives holds: (I) the gradient of the objective function is different from zero over the solution set, and the normalized gradient is constant over it; (II) the gradient of the objective function is equal to zero over the solution set. As a consequence, we obtain characterizations of the solution set of a program with a continuously differentiable and quasiconvex objective function, provided that one of the solutions is known. We also derive Lagrange multiplier characterizations of the solutions set of an inequality constrained problem with continuously differentiable objective function and differentiable constraints, which are all quasiconvex on some convex set, not necessarily open. We compare our results with the previous ones. Several examples are provided. More... »

PAGES

144-162

References to SciGraph publications

  • 2013-04. Characterizations of the solution set for a class of nonsmooth optimization problems in OPTIMIZATION LETTERS
  • 2013-07. Optimality Conditions and Characterizations of the Solution Sets in Generalized Convex Problems and Variational Inequalities in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2011-12. Characterizations of the solution sets of pseudoinvex programs and variational inequalities in JOURNAL OF INEQUALITIES AND APPLICATIONS
  • 1873-03. Ueber die Auflösung linearer Gleichungen mit reellen Coefficienten in MATHEMATISCHE ANNALEN
  • 2010-09. Optimization and Variational Inequalities with Pseudoconvex Functions in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2015-07. Characterizations of the solution set for quasiconvex programming in terms of Greenberg–Pierskalla subdifferential in JOURNAL OF GLOBAL OPTIMIZATION
  • 2013-11. Characterizations of pseudoconvex functions and semistrictly quasiconvex ones in JOURNAL OF GLOBAL OPTIMIZATION
  • 1995-12. On characterizing the solution sets of pseudolinear programs in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2003-06. Characterization of Solution Sets of Quasiconvex Programs in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2008-07. Characterizations of optimal solution sets of convex infinite programs in TOP
  • 2017-12. Characterizations of the solution set for non-essentially quasiconvex programming in OPTIMIZATION LETTERS
  • 2004-10. Lagrange Multiplier Conditions Characterizing the Optimal Solution Sets of Cone-Constrained Convex Programs in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2009-03. On Characterizing the Solution Sets of Pseudoinvex Extremum Problems in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
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    http://scigraph.springernature.com/pub.10.1007/s10957-018-1379-1

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    http://dx.doi.org/10.1007/s10957-018-1379-1

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    https://app.dimensions.ai/details/publication/pub.1106325590


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