Ghaznavi, M., Azizi, Z. (2017). An algorithm for approximating nondominated points of convex multiobjective optimization problems. Bulletin of the Iranian Mathematical Society, 43(5), 1399-1415.

M. Ghaznavi; Z. Azizi. "An algorithm for approximating nondominated points of convex multiobjective optimization problems". Bulletin of the Iranian Mathematical Society, 43, 5, 2017, 1399-1415.

Ghaznavi, M., Azizi, Z. (2017). 'An algorithm for approximating nondominated points of convex multiobjective optimization problems', Bulletin of the Iranian Mathematical Society, 43(5), pp. 1399-1415.

Ghaznavi, M., Azizi, Z. An algorithm for approximating nondominated points of convex multiobjective optimization problems. Bulletin of the Iranian Mathematical Society, 2017; 43(5): 1399-1415.

An algorithm for approximating nondominated points of convex multiobjective optimization problems

^{1}Faculty of Mathematics, Shahrood University of Technology, Shahrood, Iran

^{2}Faculty of Mathematics, Shahrood University of Technology, Shahrood, Iran.

Receive Date: 28 August 2015,
Revise Date: 20 June 2016,
Accept Date: 26 June 2016

Abstract

In this paper, we present an algorithm for generating approximate nondominated points of a multiobjective optimization problem (MOP), where the constraints and the objective functions are convex. We provide outer and inner approximations of nondominated points and prove that inner approximations provide a set of approximate weakly nondominated points. The proposed algorithm can be applied for differentiable or nondifferentiable convex MOPs. To illustrate efficiency of the proposed algorithm for convex MOPs, we provide numerical examples.

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