We address conditions for global convergence and worst-case complexity bounds of descent algorithms in nonconvex multi-objective optimization. Specifically, we define the concept of steepest-descent-related directions. We consider iterative algorithms taking steps along such directions, selecting the stepsize according to a standard Armijo-type rule. We prove that methods fitting this framework automatically enjoy global convergence properties. Moreover, we show that a slightly stricter property, satisfied by most known algorithms, guarantees the same complexity bound of as the steepest descent method.

Convergence and complexity guarantees for a wide class of descent algorithms in nonconvex multi-objective optimization / Lapucci, Matteo. - In: OPERATIONS RESEARCH LETTERS. - ISSN 0167-6377. - ELETTRONICO. - 54:(2024), pp. 107115.0-107115.0. [10.1016/j.orl.2024.107115]

Convergence and complexity guarantees for a wide class of descent algorithms in nonconvex multi-objective optimization

Lapucci, Matteo
2024

Abstract

We address conditions for global convergence and worst-case complexity bounds of descent algorithms in nonconvex multi-objective optimization. Specifically, we define the concept of steepest-descent-related directions. We consider iterative algorithms taking steps along such directions, selecting the stepsize according to a standard Armijo-type rule. We prove that methods fitting this framework automatically enjoy global convergence properties. Moreover, we show that a slightly stricter property, satisfied by most known algorithms, guarantees the same complexity bound of as the steepest descent method.
2024
54
0
0
Lapucci, Matteo
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1358085
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