求解非线性规划的序列有理规划SRP方法

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。     

SQP技术与广义投影相结合的次可行方向法

本文建立非线性不等式约束优化的一个新算法，分析和证明了算法的整体收敛性和超线性收敛性。其技巧在于将广义投影和ＳＱＰ技术结合使用。     

混合约束下广义几何规划的一种SQP算法

针对带等式和不等式约束的广义几何规划问题，构造了一种ＳＱＰ算法并证明了该算法的全局收敛性和局部二阶收敛性。     

AN EFFECTIVE SEQUENTIAL QUADRATIC PROGRAMMING ALGORITHM FOR NONLINEAR OPTIMIZATION PROBLEMS

In this paper,a new globally convergent algorithm for nonlinear optimization prablems with equality and inequality constraints is presented. The new algorithm is of SQP type which determines a search direction by solving a quadratic programming subproblem per itera-tion. Some revisions on the quadratic programming subproblem have been made in such a way that the associated constraint region is nonempty for each point x generated by the algorithm, i. e. , the subproblems always have optimal solutions. The new algorithm has two important properties. The computation of revision parameter for guaranteeing the consistency of quadratic sub-problem and the computation of the second order correction step for superlinear convergence use the same inverse of a matrix per iteration, so the computation amount of the new algorithm will not be increased much more than other SQP type algorithms; Another is that the new algorithm can give automatically a feasible point as a starting point for the quadratic subproblems pe     

非线性均衡问题一个超线性收敛的光滑逼近SQP算法

研究非线性均衡问题,引入一个磨光算子将原问题转化为光滑问题,并用此光滑问题来逼近原来的问题而求解.在每步迭代中,通过转轴运算,求解一个线性约束二次规划问题和显式修正方向来得到主方向,并通过一个显式公式来得到高阶修正方向使得算法避免Maratos效应.在不需要上层互补条件下证明了算法具有全局收敛性和强收敛性且具有超线性收敛速度.     

On-line optimization design of sliding mode guidance law with multiple constraints

The design of terminal guidance law with impact angle constraint is required for air-to-ground guided weapons to increase their warhead effect. The variable structure guidance law that consists of diving plane guidance and turning plane guidance equations with impact angle constraint is derived, and the saturation function is introduced into the design of reaching law control to weaken the chattering of the guidance system. The influence of four guidance parameters (i.e., reaching law factor, switching item gain, angle error item factor, and boundary layer thickness) on guidance performance is studied and three typical constraints (i.e., heating rate, normal load factor, and dynamic pressure) are analyzed. An optimization model is established for this problem and the feasibility of on-line optimization on guidance law parameters by the Sequential Quadratic Programming (SQP) algorithm is discussed as well. Simulation results show that the on-line optimization of the derived guidance law not only satisfies specified constraints, but also minimizes the fuel cost during the flying course. Moreover, the optimization process can be completed in a few seconds so that it is suitable for on-board applications.     

非线性互补约束均衡问题的一个滤子SQP算法

提出了—个求解非线性互补约束均衡问题的滤子SQP算法.借助Fischer-Burmeister函数把均衡约束转化为—个非光滑方程组,然后利用逐步逼近和分裂思想,给出—个与原问题近似的一般的约束优化.引入滤子思想,避免了罚函数法在选择罚因子上的困难.在适当的条件下证明了算法的全局收敛性,部分的数值结果表明算法是有效的.     

A robust SQP method based on a smoothing lower order penalty function†

Based on a smoothing approximation of a lower order penalty function and following Facchinei's method of dealing with the inconsistency of subproblems in SQP methods, we present a new robust SQP algorithm for solving a nonlinear constrained optimization problem. The proposed algorithm incorporates automatic adjustment rules for the choice of parameters. Under a new regularity condition at infeasible points, the algorithm is proved to be globally convergent.     

A SQP METHOD FOR GENERAL NONLINEAR COMPLEMENTARITY PROBLEMS

§ 1　 IntroductionThe nonlinear complementarity problem(NCP) is to find a pointx∈Rn such thatx Tf(x) =0 ,x≥ 0 ,f(x)≥ 0 ,(1 .1 )where f is a continuously differentiable function from Rninto itself.It is well known thatthe NCP is equivalent to a system of smoothly nonlinear equations with nonnegative con-straintsH (z)∶ =y -f(x)x . y =0 ,s.t. x≥ 0 ,y≥ 0 ,(1 .2 )where z=(x,y) and x y=(x1 y1 ,...,xnyn) T.Based on the above reformulation,many in-terior-point methods are established;see,fo…