以替代平面輔助之無微分最佳化演算法的收斂分析

Abstract

如何找出連續函數的極値是本論文所探討的最佳化問題。首先，針對自適區域調整演算法其收斂性證明不完整的部分予以補足。再來，提出新的演算法，結合影像處理和最佳化領域，將影像處理應用於最佳化問題，而經由此種方式所建構出的替代平面，與目標函數圖形具有高度的相似性，並可反映出函數圖形的主要特徵。最後，提出估計最小點位置的充分條件；亦即，經由一系列點收斂至目標函數圖形的替代平面，則目標函數的極値點將可被估計出。

This paper investigates a method for solving optimization problems to find the minimizers of a function. To this end, the algorithm derived from image process generates a surrogate surface to pick initial points and then estimates the minimizers. Results indicated that the surrogate surface is similar to the real one. The minimal points can be correctly estimated in diversified cases. The algorithm is adaptive on constructing a surrogate surface preserving the main feature of the real one. Moreover, this paper gives complete convergence analysis on the Adoptive Search Regions Method and states that the minimizer of a function can be estimated by specific surrogate surfaces.