Two adaptive nonmonotone trust-region algorithms for solving multiobjective optimization problems

Abstract

ABSTRACT This paper attempts to propose two adaptive nonmonotone trust-region algorithms in the multiobjective optimization (MO) case. The first proposed trust-region algorithm uses a modified maximum nonmonotone technique, which takes a convex combination of the maximum value of some preceding successful iterates and the function value in the current iterate. The second one employs the average nonmonotone technique, which takes a weighted average of the successive function values. Under some suitable assumptions, the convergence of the sequences generated by the trust-region algorithms that use the aforementioned nonmonotone techniques to a critical point is shown. Using some well-known test problems, we compare our proposed adaptive nonmonotone MO algorithms with some other MO trust-region algorithms. To conduct a thorough comparison in this regard, some performance criteria are used. These numerical results confirm a significant advantage of applying the proposed adaptive nonmonotone trust-region algorithms in solving MO problems. Finally, the proposed algorithms are implemented to optimize one of the optimization problems of the abrasive water-jet machining process.