A Proximal Point-Type Method for Multicriteria Optimization

作者：Bento G C^*; Cruz Neto J X; Soubeyran A

来源：Set-Valued and Variational Analysis, 2014, 22(3): 557-573.

DOI：10.1007/s11228-014-0279-2

• Proximal
• Multicriteria optimization
• Quasi-convexity
• Fejer convergence
• Weak sharp

In this paper, we present a proximal point algorithm for multicriteria optimization, by assuming an iterative process which uses a variable scalarization function. With respect to the convergence analysis, firstly we show that, for any sequence generated from our algorithm, each accumulation point is a Pareto critical point for the multiobjective function. A more significant novelty here is that our paper gets full convergence for quasi-convex functions. In the convex or pseudo-convex cases, we prove convergence to a weak Pareto optimal point. Another contribution is to consider a variant of our algorithm, obtaining the iterative step through an unconstrained subproblem. Then, we show that any sequence generated by this new algorithm attains a Pareto optimal point after a finite number of iterations under the assumption that the weak Pareto optimal set is weak sharp for the multiobjective problem.

• 出版日期2014-9