求解非线性规划的序列有理规划SRP方法

A Sequential Rational Programming Method for Solving Nonlinear Programming Based on a Rational Approximation at Two Expanded Points

基于分子、分母皆线性的两点有理逼近，本文对于非线性规划提出了序列有理规划ＳＲＰ方法，按两种情况进行了研究。第一种为ＳＲＰ－Ｌ方法，将原问题化为等效的ＬＰ问题求解；第二种为ＳＲＰ－Ｑ方法，将原问题化为等效的ＱＰ问题求解。本文的工作说明，两点有理逼近函数对于改进优化方法是有益的。

Based on a RATP(Rational Approximation with linear numerator and deominator func-tion at Two expanded Points),this paper proposes SRP(Sequential Rational Programming)method to solve nonlinear programming which is studied in two cases. First, a method calledSRP-L is proposed to approach the objective function as linear Taylor’s expansion and con-strained functions as RATP’s expansion by using the present point’s function value and bothof the present and predecessive points’ gradient information, then the primary problem isturned into equivalent linear programming. Numerical examples show that the convergentrate of the method is much faster than that of the SLP method. Second, a method calledSRP-Q is proposed to approach the objective function as a second-order Taylor’s expansionand constraits as the same forms of the SRP-L method ,then the primary problem is turnedinto equivalent quadratic programming. The method is implemented in structural optimiza-tion program of the truss problem and obtains an expectant effect.It shows that the methodis more potentiality than that of the SQP method.