Nonsmooth multiobjective programming: strong Kuhn–Tucker conditions

Nonsmooth multiobjective programming: strong Kuhn–Tucker conditions We consider a multiobjective optimization problem with a feasible set defined by inequality and equality constraints and a set constraint, where the objective and constraint functions are locally Lipschitz. Several constraint qualifications are given in such a way that they generalize the classical ones, when the functions are differentiable. The relationships between them are analyzed. Then, we establish strong Kuhn–Tucker necessary optimality conditions in terms of the Clarke subdifferentials such that the multipliers of the objective function are all positive. Furthermore, sufficient optimality conditions under generalized convexity assumptions are derived. Moreover, the concept of efficiency is used to formulate duality for nonsmooth multiobjective problems. Wolf and Mond–Weir type dual problems are formulated. We also establish the weak and strong duality theorems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Nonsmooth multiobjective programming: strong Kuhn–Tucker conditions

Loading next page...
 
/lp/springer_journal/nonsmooth-multiobjective-programming-strong-kuhn-tucker-conditions-WR74cwsdCA
Publisher
Springer Journals
Copyright
Copyright © 2012 by Springer Basel AG
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-012-0201-9
Publisher site
See Article on Publisher Site

Abstract

We consider a multiobjective optimization problem with a feasible set defined by inequality and equality constraints and a set constraint, where the objective and constraint functions are locally Lipschitz. Several constraint qualifications are given in such a way that they generalize the classical ones, when the functions are differentiable. The relationships between them are analyzed. Then, we establish strong Kuhn–Tucker necessary optimality conditions in terms of the Clarke subdifferentials such that the multipliers of the objective function are all positive. Furthermore, sufficient optimality conditions under generalized convexity assumptions are derived. Moreover, the concept of efficiency is used to formulate duality for nonsmooth multiobjective problems. Wolf and Mond–Weir type dual problems are formulated. We also establish the weak and strong duality theorems.

Journal

PositivitySpringer Journals

Published: Sep 7, 2012

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off