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1. A new nonmonotone filter Barzilai–Borwein method for solving unconstrained optimization problems.

Author

Arzani, F. and Peyghami, M. Reza

Subjects
*MONOTONE operators, *MATHEMATICAL optimization, *ALGORITHMS, *STOCHASTIC convergence, *NUMERICAL analysis, *MATHEMATICAL analysis
Abstract

In this paper, a finite filter is used in the structure of the Barzilai–Browein (BB) gradient method in order to propose a new modified BB algorithm for solving large-scale unconstrained optimization problems. Our algorithm is equipped with a relaxed nonmonotone line search technique which allows the algorithm to enjoy the nonmonotonicity properties from scratch. Under some suitable conditions, the global convergence property of the new proposed algorithm is established. Numerical results on some test problems in CUTEr library show the efficiency and effectiveness of the new algorithm in practice too. [ABSTRACT FROM PUBLISHER]

Published
2016
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2. Trust region methods for solving multiobjective optimisation.

Author

Qu, Shaojian, Goh, Mark, and Liang, Bing

Subjects
*PROBLEM solving, *MATHEMATICAL optimization, *ALGORITHMS, *STOCHASTIC convergence, *NONSMOOTH optimization, *MATHEMATICAL analysis, *NUMERICAL analysis
Abstract

This paper first proposes a trust region algorithm to obtain a stationary point of unconstrained multiobjective optimisation problem. Under suitable assumptions, the global convergence of the new algorithm is established. We then extend the trust region method to solve the non-smooth multiobjective optimisation problem. [ABSTRACT FROM PUBLISHER]

Published
2013
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