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Interval-valued optimization problems involving (α, ρ)-right upper-Dini-derivative functions.

Vasile Preda1

  • 1Faculty of Mathematics and Computer Science, University of Bucharest, 010014 Bucharest, Romania ; Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, 050711 Bucharest, Romania ; National Institute of Economic Research, 050711 Bucharest, Romania.

Thescientificworldjournal
|July 2, 2014
PubMed
Summary
This summary is machine-generated.

This study establishes optimality conditions for interval-valued multiobjective problems using a novel Dini-derivative. Duality results are also presented for Wolfe and Mond-Weir duals.

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Area of Science:

  • Optimization Theory
  • Mathematical Analysis

Background:

  • Multiobjective optimization problems involve multiple conflicting objectives.
  • Interval-valued problems introduce uncertainty and complexity.
  • Existing optimality conditions often require strong convexity assumptions.

Purpose of the Study:

  • To establish necessary and sufficient optimality conditions for weak efficient solutions in interval-valued multiobjective problems.
  • To introduce and utilize new generalized convexities.
  • To investigate duality theorems for these problems.

Main Methods:

  • Employing the tool-right upper-Dini-derivative, an extension of the directional derivative.
  • Developing new generalized convexity concepts.
  • Applying these tools to derive optimality and duality results.

Main Results:

  • Established necessary and sufficient optimality conditions for weak efficient solutions.
  • Demonstrated the effectiveness of the new generalized convexities.
  • Proved duality results for Wolfe and Mond-Weir duals within this framework.

Conclusions:

  • The proposed Dini-derivative and generalized convexities offer a powerful framework for analyzing interval-valued multiobjective problems.
  • The established conditions and duality results extend existing theory.
  • This work provides valuable theoretical insights for optimization research.