Adaptive Search Regions in Derivative Free Optimization Problems

• Main Authors: Lien-Chi Lai, 賴鍊奇
• Other Authors: Weichung Wang
• Format: Others
• Language: en_US
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/78861635237905202838

碩士 === 國立高雄大學 === 應用數學系碩士班 === 96 === This article attempts to find all local minima in an experimental region of interest. The optimization problems of interest are characterized as follows. First, the function is either complicated or defined implicitly. Second, the computational cost associated with simulating the function values is very high. We develop a new framework suited not only to accurate location of a given minimum, but also to finding multiple local minima automatically. In this aim, the algorithm first determines an approximate surrogate surface. Next, the algorithm shrinks the search region, refines the grids and then uses a specific form of retracing over the experimental region. The algorithm includes an asymptotic convergence analysis for each local minimum as well as a theoretical global dense searching to ensure that all local minima and the global minimum can be found. The numerical results produced by the algorithm are seen to perform well, even for oscillatory models and high-dimensional problems.