TAILIEUCHUNG - On a second order step-size algorithm

In this paper we present a modification of the second-order step-size algorithm. This modification is based on the so called "forcing functions". It is proved that this modified algorithm is well-defined. It is also proved that every point of accumulation of the sequence generated by this algorithm is a second-order point of the nonlinear programming problem. | Yugoslav Journal of Operations Research 12 (2002), Number 1, 121-127 ON A SECONDSTEP EPSECOND-ORDER ST EP-SIZE ALGORITHM* Nada I. DJURANOVI]-MILI^I] Department of Mathematics Faculty of Technology and Metallurgy University of Belgrade, Belgrade, Yugoslavia nmilicic@ Abstract: In this paper we present a modification of the second-order step-size algorithm. This modification is based on the so called "forcing functions". It is proved that this modified algorithm is well-defined. It is also proved that every point of accumulation of the sequence generated by this algorithm is a second-order point of the nonlinear programming problem. Two different convergence proofs are given having in mind two interpretations of the presented algorithm. Keywords: Forcing function, step-size algorithm, second-order conditions. 1. INTRODUCTION We are concerned with the following problem of the unconstrained optimization: min{ϕ ( x)

• Kỹ thuật lập trình
• Forcing function
• Step size algorithm
• Second order conditions
• Nonlinear programming problem
• Presented algorithm