Volume 43, pp. 21-44, 2014-2015.

A moving asymptotes algorithm using new local convex approximation methods with explicit solutions

Mostafa Bachar, Thierry Estebenet, and Allal Guessab


In this paper we propose new local convex approximations for solving unconstrained non-linear optimization problems based on a moving asymptotes algorithm. This method incorporates second-order information for the moving asymptotes location. As a consequence, at each step of the iterative process, a strictly convex approximation subproblem is generated and solved. All subproblems have explicit global optima. This considerably reduces the computational cost of our optimization method and generates an iteration sequence. For this method, we prove convergence of the optimization algorithm under basic assumptions. In addition, we present an industrial problem to illustrate a practical application and a numerical test of our method.

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Key words

geometric convergence, nonlinear programming, method of moving asymptotes, multivariate convex approximation

AMS subject classifications

65K05, 65K10, 65L10, 90C30, 46N10

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