Set-Valued and Variational Analysis

, Volume 23, Issue 3, pp 519–546 | Cite as

Convex SIP Problems with Finitely Representable Compact Index Sets: Immobile Indices and the Properties of the Auxiliary NLP Problem

  • O. I. Kostyukova
  • T. V. TchemisovaEmail author


In the paper, we consider a problem of convex Semi-Infinite Programming with a compact index set defined by a finite number of nonlinear inequalities. While studying this problem, we apply the approach developed in our previous works and based on the notions of immobile indices, the corresponding immobility orders and the properties of a specially constructed auxiliary nonlinear problem. The main results of the paper consist in the formulation of sufficient optimality conditions for a feasible solution of the original SIP problem in terms of the optimality conditions for this solution in a specially constructed auxiliary nonlinear programming problem and in study of certain useful properties of this finite problem.


Semi-infinite programming (SIP) Constraint qualifications (CQ) Lower level problem (SIP) Immobile index Immobility order Optimality conditions Nonlinear programming (NLP) 

Mathematics Subject Classification (2010)

90C25 90C30 90C34 


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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Institute of MathematicsNational Academy of Sciences of BelarusMinskBelarus
  2. 2.CIDMA–Center for Research and Development in Mathematics and Applications, Department of MathematicsUniversity of Aveiro, Campus University SantiagoAveiroPortugal

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