初始點(diǎn)任意的解非線性不等式約束優(yōu)化問題的結(jié)合共軛梯度參數(shù)的超記憶梯度廣義投影算法-在線瀏覽
2025-05-11 12:38本頁面
【正文】 GENERALIZED SUPERMEMORY GRADIENT PROJECTION METHOD WITH ARBITRARY INITIAL POINT AND CONJUGATE GRADIENT SCALAR FOR NONLINEAR PROGRAMMING WITH NONLINEAR INEQUALITY CONSTRAINTSSun Qingying，liu xinhaiDepart. of Applied Mathematics, University of petroleum, Dongying, 257061Abstract In this paper, by using generalized projection matrix, conditions are given on the scalars in the supermemory gradient direction to ensure that the supermemory gradient projection direction is a descent direction. A generalized supermemory gradient projection method with arbitrary initial point for nonlinear programming with nonlinear inequality constraints is presented. The global convergence properties of the new method are discussed. Combining with conjugate gradient scalar with our new method, a new class of generalized supermemory gradient projection methods with conjugate gradient scalar is presented. The numerical results illustrate that the new methods are effective.Key words: Nonlinear programming, General projection, Nonlinear inequality constraints, Supermemory gradient, Arbitrary initial point, Convergence 關(guān)鍵詞: 非線性規(guī)劃，廣義投影, 非線性不等式約束，超記憶梯度，任意初始點(diǎn), 收斂1. 引言 梯度投影法是求解非線性約束最優(yōu)化問題的基本方法之一，在最優(yōu)化領(lǐng)域占有重要地位[1~6]. 如高自友在文[3]中建立了求解非線性不等式約束優(yōu)化問題的計算量小，算法穩(wěn)定的任意初始點(diǎn)下的廣義梯度投影算法, 但算法收斂速度慢. 超記憶梯度算法是求解無約束規(guī)劃的有效算法. 這類方法在迭代中較多地利用了已經(jīng)得到的目標(biāo)函數(shù)的某些信息，因而具有較快的收斂速度[7~8]. 若能將此法推廣用于求解約束優(yōu)化問題，可望改善現(xiàn)有算法的收斂速度. 高自友在文[9] 建立了求解非線性不等式約束優(yōu)化問題的超記憶梯度算法. 時貞軍[10,11]對無約束規(guī)劃（p）提出了一種參數(shù)取值為區(qū)間的改進(jìn)共軛梯度算法，并在水平集有界的條件下證明了算法的收斂性質(zhì). 受文獻(xiàn)[9, 10, 11]的啟發(fā)，本文利用廣義投影矩陣，對求解無約束規(guī)劃的超記憶梯度算法中的參數(shù)給出一種新的取值范圍以保證得到目標(biāo)函數(shù)的超記憶梯度廣義投影下降方向，并與處理任意初始點(diǎn)的方法技巧結(jié)合建立求解非線性不等式約束優(yōu)化問題的一個初始點(diǎn)任意的超記憶梯度廣義投影算法，并在較弱條件下證明算法的收斂性. 同時給出具有好的收斂性質(zhì)的結(jié)合FR，P
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