Image Space Analysis to Lagrange-Type Duality for Constrained Vector Optimization Problems with Applications

Shengkun Zhu ()
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Shengkun Zhu: Southwestern University of Finance and Economics

Journal of Optimization Theory and Applications, 2018, vol. 177, issue 3, No 9, 743-769

Abstract: Abstract The main purpose of this paper is to study the duality and penalty method for a constrained nonconvex vector optimization problem. Following along with the image space analysis, a Lagrange-type duality for a constrained nonconvex vector optimization problem is proposed by virtue of the class of vector-valued regular weak separation functions in the image space. Simultaneously, some equivalent characterizations to the zero duality gap property are established including the Lagrange multiplier, the Lagrange saddle point and the regular separation. Moreover, an exact penalization is also obtained by means of a local image regularity condition and a class of particular regular weak separation functions in the image space.

Keywords: Image space analysis; Vector optimization; Lagrange-type duality; Exact penalization; Image regularity condition; 49N15; 90C30; 90C46 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-016-1027-6

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