Title: Duality of control problems in general Banach spaces

Authors: Pramoda Kumar Behera; Saroj Kumar Padhan; Chandal Nahak

Addresses: Department of Mathematics, Veer Surendra Sai University of Technology, Burla-768018, India ' Department of Mathematics, Veer Surendra Sai University of Technology, Burla-768018, India ' Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur-721302, India

Abstract: Control problems have been given a special attention to the theory of optimisation, which is concerned with problems involving infinite dimensional cases. Control problems along with various types of their duals are described in general Banach spaces. Under convexity assumptions on functionals, several duality (weak, strong and converse) results are established between control primal and the corresponding Mangasarian type dual problem. Again, the Mond-Weir type duality model is constructed to weaken the convexity condition to pseudo-convexity and quasi-convexity. Many nontrivial examples are given to support the efficacy of the new findings. It is found that some of earlier results are the special cases of the present investigations.

Keywords: control problems? convexity? Mangasarian type duality? Mond-Weir type duality.

DOI: 10.1504/IJOR.2021.119408

International Journal of Operational Research, 2021 Vol.42 No.3, pp.358 - 370

Accepted: 05 Jun 2019
Published online: 03 Dec 2021 *

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