An Algorithm Combining Moving Asymptotes With Conjugate Gradient For Large-scale Unconstrained Optimization

The method of moving asymptotes (MA) is a kind of new optimization method which isproposed especially for solving structure optimization problems in engineering initially. Afterwardsthis method was further studied and developed; it works well in solving large-scale unconstrainedoptimization problems. Conjugate gradient method is one of the most effective common methods forlarge-scale optimization for its simplicity. Combining the two methods, we expect the new hybridmethod performs better. In this paper, we give a new MA model with new moving asymptotes andrelated parameters, then propose an algorithm of moving asymptotes combining conjugate gradientfor solving unconstrained optimization problem with the basic theory of spectral conjugate gradientmethod (or the scaled BFGS preconditioned conjugate gradient algorithm). At last we prove theconvergence of the new algorithm and carry out the numerical experiments.The paper is divided into five chapters. In the first chapter we briefly introduce the issues ofoptimization and the contents of this paper. In the second chapter we describe the development of themethod of moving asymptotes and the conjugate gradient methods. We give the basis and structure ofthe search direction of the new algorithm, discuss the choice of the parameters in it and analyze itsdecent property in the third chapter. In the fourth chapter, we give a description of the new algorithmof moving asymptotes combining conjugate gradient for solving unconstrained optimization problemand prove its convergence under some conditions. In the fifth chapter we give some numericalcomparison experiments about the algorithms in the fourth chapter, analyze the numerical results, andeduce some useful conclusions. The theoretic and numerical results show finally that the algorithm inthis paper is efficient and promising.