Object structure

Title:

Well Posedness and Lipschitzness of Solutions in Vector Optimization

Subtitle:

Raport Badawczy = Research Report ; RB/77/2003

Creator:

Bednarczuk, Ewa Małgorzata. Autor

Publisher:

Instytut Badań Systemowych. Polska Akademia Nauk ; Systems Research Institute. Polish Academy of Sciences

Place of publishing:

Warszawa

Date issued/created:

2003

Description:

13 pages ; 21 cm ; Bibliography p. 12-13

Subject and Keywords:

Vector optimization ; Optymalizacja wektorowa ; Lipschitz continuity ; Ciągłość lipschitza

Abstract:

In the present paper we investigate the concept of strict and strong solutions to vector optimization problems. When applied to scalar optimization problems, these concepts both reduce to the concept of weak sharp minima due to Poliak and investigated by many authors. We prove calmness of solutions to parametric vector optimization problems at points which are strict and strong. In the class of well-posed problems we study conditions ensuring Lipschitz and/or Hölder continuity of efficient solutions to parametric vector optimization problems. We prove that in the case where calmness of the solution set-valued mapping S at some solution x0 is of interest it is enough to assume that the solution set is simultaneously. Strict and strong around x0.In the present paper we investigate the concept of strict and strong solutions to vector optimization problems. When applied to scalar optimization problems, these concepts both reduce to the concept of weak sharp minima due to Poliak and investigated by many authors. We prove calmness of solutions to parametric vector optimization problems at points which are strict and strong. In the class of well-posed problems we study conditions ensuring Lipschitz and/or Hölder continuity of efficient solutions to parametric vector optimization problems. We prove that in the case where calmness of the solution set-valued mapping S at some solution x0 is of interest it is enough to assume that the solution set is simultaneously. Strict and strong around x0.

Relation:

Raport Badawczy = Research Report

Resource Type:

Report

Source:

RB-2003-77

Language:

eng

Language of abstract:

eng

Rights:

Creative Commons Attribution BY 4.0 license

Terms of use:

Copyright-protected material. [CC BY 4.0] May be used within the scope specified in Creative Commons Attribution BY 4.0 license, full text available at: ; -

Digitizing institution:

Systems Research Institute of the Polish Academy of Sciences

Original in:

Library of Systems Research Institute PAS

Projects co-financed by:

Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.


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https://www.ibspan.waw.pl/~alex/OZwRCIN/WA777_112414_RB-2003-77_Well%20Posedness%20and%20Lipschitzness%20of%20Solutions%20in%20Vector%20Optimization_content.pdf
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