A SURVEY ON MULTIOBJECTIVE DESCENT METHODS

Author(s)

Ellen H. Fukuda ^[1] ; Luis Mauricio Graña Drummond ^[2]

Affiliation

^[1] Kyoto University. Graduate School of Informatics - Japão

^[2] Kyoto University. Graduate School of Informatics - Japão

• Document type: Journal article
• Source: Pesquisa Operacional; v. 34, n. 3, p. 585-620, 2014-12-00.

Abstract

We present a rigorous and comprehensive survey on extensions to the multicriteria setting of three well-known scalar optimization algorithms. Multiobjective versions of the steepest descent, the projected gradient and the Newton methods are analyzed in detail. At each iteration, the search directions of these methods are computed by solving real-valued optimization problems and, in order to guarantee an adequate objective value decrease, Armijo-like rules are implemented by means of a backtracking procedure. Under standard assumptions, convergence to Pareto (weak Pareto) optima is established. For the Newton method, superlinear convergence is proved and, assuming Lipschitz continuity of the objectives second derivatives, it is shown that the rate is quadratic (AU)

• FAPESP's process: 10/20572-0 - Exact penalties for nonlinear optimization and second-order cone programming
• Grantee: Ellen Hidemi Fukuda
• Support Opportunities: Scholarships in Brazil - Post-Doctoral