1,090 research outputs found
Tangential Extremal Principles for Finite and Infinite Systems of Sets, II: Applications to Semi-infinite and Multiobjective Optimization
This paper contains selected applications of the new tangential extremal
principles and related results developed in Part I to calculus rules for
infinite intersections of sets and optimality conditions for problems of
semi-infinite programming and multiobjective optimization with countable
constraint
Optimality conditions in convex multiobjective SIP
The purpose of this paper is to characterize the weak efficient solutions, the efficient solutions, and the isolated efficient solutions of a given vector optimization problem with finitely many convex objective functions and infinitely many convex constraints. To do this, we introduce new and already known data qualifications (conditions involving the constraints and/or the objectives) in order to get optimality conditions which are expressed in terms of either Karusk–Kuhn–Tucker multipliers or a new gap function associated with the given problem.This research was partially cosponsored by the Ministry of Economy and Competitiveness (MINECO) of Spain, and by the European Regional Development Fund (ERDF) of the European Commission, Project MTM2014-59179-C2-1-P
Implicit optimality criterion for convex SIP problem with box constrained index set
We consider a convex problem of Semi-Infinite Programming (SIP) with multidimensional
index set. In study of this problem we apply the approach suggested in [20] for
convex SIP problems with one-dimensional index sets and based on the notions of immobile
indices and their immobility orders. For the problem under consideration we formulate
optimality conditions that are explicit and have the form of criterion. We compare this
criterion with other known optimality conditions for SIP and show its efficiency in the
convex case
On the algorithm of determination of immobile indices for convex SIP problems
We consider convex Semi-Infinite Programming (SIP) problems with a continuum
of constraints. For these problems we introduce new concepts of immobility
orders and immobile indices. These concepts are objective and important characteristics
of the feasible sets of the convex SIP problems since they make it possible
to formulate optimality conditions for these problems in terms of optimality conditions
for some NLP problems (with a finite number of constraints). In the paper we
describe a finite algorithm (DIO algorithm) of determination of immobile indices
together with their immobility orders, study some important properties of this algorithm,
and formulate the Implicit Optimality Criterion for convex SIP without any
constraint qualification conditions (CQC). An example illustrating the application
of the DIO algorithm is provided
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