روش تجزيه جريمه اي براي مسائل بهينه سازي چند هدفه مقيد عدد اصلى

Multi-objective optimization , Cardinality constraints , Penalty decomposition , Portfolio selec‎tion problem , Pareto optimal

A penalty decomposition approach for multiobjective cardinality-constrained optimization problems

رياضي كاربردي و علوم كامپيوتر

In this thesis, we consider multi-objective optimization problems with a cardinality constraint on the vector of decision variables an‎d linear constraints. For this class of problems, we analyze necessary an‎d sufficient conditions of Pareto optimality. We afterwards propose a Penalty Decomposition type algorithm, exploiting multi-objective descent methods, to tackle the aforementioned family of problems. We conduct a rigorous convergence analysis for the proposed method, where we prove that the produced sequence of points has limit points, each one being feasible an‎d satisfying first-order optimality conditions. Moreover, computational experiments, carried out on instances of relevant real-world problems such as sparse mean/variance portfolio selec‎tion an‎d sparse regularized logistic regression, in their multi-objective formulation, show that the proposed procedure is effective at finding solutions forming good Pareto sets approximations.

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