Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.11.2027.1.06

Volume 11, Issue 1, 1 February 2027, Pages 115-132

 

Abstract. In this paper, we focus on a multiobjective convex optimization problem constrained by a closed convex set. We develop a Newton type method for such a problem. The key step here is to solve subproblems involving Bregman distances along with the quadratic approximations of the objective functions at the given iterate. These subproblems allow us to generate descent directions and an Armijo type rule is used to furnish a step length. We also show that, under mild assumptions, the sequence of iterates generated by the algorithm converges to a critical point, providing us with a weak Pareto minimizer.

 

How to Cite this Article:
M.A.T. Ansary, J. Dutta, Newton’s methods using Bregman functions for convex multiobjective optimization, J. Nonlinear Var. Anal. 11 (2027), 115-132.