Superlinear Convergence of a Modified Newton's Method for Convex Optimization Problems With Constraints

Bouchta Rhanizar

Journal of Mathematics Research, 2021, vol. 13, issue 2, 90

Abstract: We consider the constrained optimization problem defined by- $$f (x^*) = \min_{x \in X} f(x)\eqno (1)$$ where the function f - \pmb{\mathbb{R}}^{n} → \pmb{\mathbb{R}} is convex on a closed bounded convex set X. To solve problem (1), most methods transform this problem into a problem without constraints, either by introducing Lagrange multipliers or a projection method. The purpose of this paper is to give a new method to solve some constrained optimization problems, based on the definition of a descent direction and a step while remaining in the X convex domain. A convergence theorem is proven. The paper ends with some numerical examples.

Date: 2021
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