A MOVING ASYMPTOTES ALGORITHM USING NEW LOCAL CONVEX APPROXIMATION METHODS WITH EXPLICIT SOLUTIONS

作者：Bachar Mostafa^*; Estebenet Thierry; Guessab Allal

来源：Electronic Transactions on Numerical Analysis, 2014, 43: 21-44.

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

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.

• 出版日期2014