一个部分有界约束非线性优化问题的无导数算法  

Derivative-free algorithm for nonlinear optimization problems with partial-bounded constraints

作　　者：孙强[1] 吕巍[1] 

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2015年第4期452-462,共11页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11101262;11171050);上海市重点学科建设资助项目(S30104);大连理工大学专项基金资助项目(DUTTX2011106)

摘　　要：在文献(Liuzzi G,Lucidi S,Sciandrone M.Sequential penalty derivative-free methods for nonlinear constrained optimization.SIAM Journal on Optimization,2010,20:2614-2635)提出的求解非线性有界约束优化问题的算法DFL(derivative-free line search algorithm)的基础上,提出了一个求解含有部分有界变量约束的非线性优化问题的无导数算法PDFA(penalty derivative-free line search algorithm).假设目标函数以及约束函数的导数由于某种原因无法得到,并且部分变量有界.与DFL不同的是,PDFA无需估计无界变量的上下界,并且沿简单边界的一组新正基进行线性搜索.证明了算法的收敛性,并用这两种算法对5个算列进行了数值计算,结果表明PDFA是有效可行的.A penalty derivative-free line search algorithm （PDFA） for nonlinear optimization problems with partial-bounded constraints is put forward based on the derivative-free line （DFL） search algorithm for nonlinear optimization problems with bounded constraints proposed in the reference （Liuzzi G, Lucidi S, Sciandrone M. Sequential penalty derivative-free methods for nonlinear constrained optimization. SIAM Journal on Optimization, 2010, 20： 2614-2635）. The PDFA works with the assumption that the derivatives of the objective function and constraint functions are unknown, and some variables are bounded. Unlike the DFL, the PDFA searches along a new positive base without estimating the bounds of the unbounded variables. The convergence to stationary points of the constrained problem is proved, and the calculation for five test problems are operated by the PDFA and the DFL. Results show that the PDFA is effective and feasible.

关 键 词：部分有界约束 非线性优化 无导数算法 

分 类 号：O221.2[理学—运筹学与控制论]