Economics at your fingertips  

Globally convergent Newton-type methods for multiobjective optimization

M. L. N. Gonçalves (), F. S. Lima () and L. F. Prudente ()
Additional contact information
M. L. N. Gonçalves: IME, Universidade Federal de Goiás
F. S. Lima: IME, Universidade Federal de Goiás
L. F. Prudente: IME, Universidade Federal de Goiás

Computational Optimization and Applications, 2022, vol. 83, issue 2, No 2, 403-434

Abstract: Abstract We propose two Newton-type methods for solving (possibly) nonconvex unconstrained multiobjective optimization problems. The first is directly inspired by the Newton method designed to solve convex problems, whereas the second uses second-order information of the objective functions with ingredients of the steepest descent method. One of the key points of our approaches is to impose some safeguard strategies on the search directions. These strategies are associated to the conditions that prevent, at each iteration, the search direction to be too close to orthogonality with the multiobjective steepest descent direction and require a proportionality between the lengths of such directions. In order to fulfill the demanded safeguard conditions on the search directions of Newton-type methods, we adopt the technique in which the Hessians are modified, if necessary, by adding multiples of the identity. For our first Newton-type method, it is also shown that, under convexity assumptions, the local superlinear rate of convergence (or quadratic, in the case where the Hessians of the objectives are Lipschitz continuous) to a local efficient point of the given problem is recovered. The global convergences of the aforementioned methods are based, first, on presenting and establishing the global convergence of a general algorithm and, then, showing that the new methods fall in this general algorithm. Numerical experiments illustrating the practical advantages of the proposed Newton-type schemes are presented.

Keywords: Multiobjective optimization; Newton method; Global convergence; Numerical experiments; 49M15; 65K05; 90C26; 90C29 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link) Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Ordering information: This journal article can be ordered from

DOI: 10.1007/s10589-022-00414-7

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().

Page updated 2022-11-27
Handle: RePEc:spr:coopap:v:83:y:2022:i:2:d:10.1007_s10589-022-00414-7