TAILIEUCHUNG - An algorithm for LC1 optimization

In this paper an algorithm for LC1 unconstrained optimization problems, which uses the second order Dini upper directional derivative is considered. The purpose of the paper is to establish general algorithm hypotheses under which convergence occurs to optimal points. A convergence proof is given, as well as an estimate of the rate of convergence. | Yugoslav Journal of Operations Research 15 (2005), Number 2, 301-306 AN ALGORITHM FOR LC1 OPTIMIZATION* Nada I. ĐURANOVIĆ-MILIČIĆ Department of Mathematics, Faculty of Technology and Metallurgy University of Belgrade, Belgrade, Yugoslavia nmilicic@ Received: January 2003 / Accepted: March 2005 Abstract. In this paper an algorithm for LC1 unconstrained optimization problems, which uses the second order Dini upper directional derivative is considered. The purpose of the paper is to establish general algorithm hypotheses under which convergence occurs to optimal points. A convergence proof is given, as well as an estimate of the rate of convergence. Keywords. Directional derivative, second order Dini upper directional derivative, uniformly convex functions. 1. INTRODUCTION We shall consider the following LC1 problem of unconstrained optimization { } min f ( x)

• Toán học
• Directional derivative
• Second order Dini upper directional derivative
• Uniformly convex functions
• Algorithm hypotheses
• Convergence proof
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