线性等式约束多目标规划的一个降维算法

本文提出具有线性等式约束多目标规划问题的一个降维算法．当目标函数全是二次或线性但至少有一个二次型时，用线性加权法转化原问题为单目标二次规划，再用降维方法转化为求解一个线性方程组．若目标函数非上述情形，首先用线性加权法将原问题转化为具有线性等式约束的非线性规划，然后，对这一非线性规划的目标函数二次逼近，构成线性等式约束二次规划序列，用降维法求解，直到满足精度要求为止．     

等式约束非线性控制系统的时程精细计算

针对等式约束非线性最优控制问题,通过一阶Taylor级数展开,得到线性化的动力学方程,进而在方程原变量的基础上,引入对偶向量(Lagrange乘子向量),将动力学方程从Lagrange体系引入到了Hamilton体系,在全状态下,从一个新的角度对等式约束非线性控制问题进行了描述,进一步基于时程精细积分理论,对其方程进行了有效的精细求解,并通过算例说明了文中方法的有效性。     

非线性等式和线性不等式约束优化的信赖域方法 *

对非线性等式和线性不等式约束的优化问题提出一个新的信赖域算法,在通常假设条件下,证明了算法的全局收敛性.此外,由于通过引进松弛变量,可把非线性不等式约束转化为一个方程的形式,因此,该算法可用于求解一般非线性规划问题.     

等式约束优化一个新的SQP算法

提出了一个处理等式约束优化问题新的SQP算法,该算法通过求解一个增广Lagrange函数的拟Newton方法推导出一个等式约束二次规划子问题,从而获得下降方向．罚因子具有自动调节性,并能避免趋于无穷．为克服Maratos效应采用增广Lagrange函数作为效益函数并结合二阶步校正方法．在适当的条件下,证明算法是全局收敛的,并且具有超线性收敛速度．     

初始点任意的一个非线性优化的广义梯度投影法

广义投影算法的优点是避免转轴运算。它成功地给出了线性约束问题、初始点任意的只带非线性不等式约束问题，以及利用辅助规划来处理带等式与不等式约束问题的算法．后者完满地解决了投影算法对于非线性等式约束问题的处理，但要求满足不等式约束的初始点．本文据此利用广义投影与罚函数技巧给出了一个初始点任意的等式与不等式约束问题的算法，省去了求初始解的计算，并保持了上述方法的优点，证明了算法的全局收敛性     

非线性最优化一个可行序列等式约束二次规划算法

本文针对非线性不等式约束优化问题,提出了一个新的可行序列等式约束二次规划算法．在每次迭代中,该算法只需求解三个相同规模且仅含等式约束的二次规划(必要时求解一个辅助的线性规划),因而其计算工作量较小．在一般的条件下,证明了算法具有全局收敛及超线性收敛性．数值实验表明算法是有效的．     

一类带等式约束非光滑最优化问题的逐次二次规划方法

本文对一类带等式的非光滑最优化问题给出了一种逐次二次规划方法。这类问题的目标函数是非光滑合成函数，约束函数是非线性光滑函数。该方法通过逐次解二阶规划寻找搜索方向，使用ｌ１－罚函数的非精确线搜索得到新的迭代点。我们证明了算法的全局收敛性并给出了数值试验结果。     

可行方向法的统一探讨：二阶段算法模型

1 引言可行方向法是非线性规划中一类思想简单数值效果好的基本方法。特别是对线性约束问题,这类方法一直受人欢迎。但由于非线性约束带来的困难,这一领域内的工作近年来并不多见。文[1]曾统一和推广了国内外文献中常见的投影梯度和既约梯度法。本文首先提出一个二阶段算法模型用来解不等式约束问题,大范围地统一和推广了现有的可行方向法。然后,对于一般非线性规划问题,本文利用仅含等式约束的Lagrange函数作为搜索函数,直接应用上述模型的结果给出相应的模型,大大推广和简化了[2]中方法。具体选     

非线性优化修正Frisch函数方法的乘子映射

对于同时含有等式与不等式约束的非线性优化问题的修正Frisch函数方法,给出其乘子映射和解映射的导数的估计.将得到的估计用于建立修正Frisch函数方法的线性收敛速率.在线性无关的约束规范,严格互补条件和二阶充分性条件成立的前提下,证得该收敛率与1/c成正比.本文的收敛性分析依赖于矩阵的奇异值分解,其方法可以用来分析其他的修正Lagrange方法.     

关于非线性等式约束优化问题的一点注记

给出了一种求解非线性约束优化问题的算法.利用Lagrange函数,将非线性约束优化问题转化为无约束优化问题,从而得到解决.方法仅仅依靠求解一个线性方程组来求解,因此使得计算量减小,计算速度变快.在一定条件下,给出算法的收敛性证明.数值试验表明方法是有效的.     

可行逐步二次规划方法解非线性方程组

We transform the system of nonlinear equations into a nonlinear programming problem, which is attacked by feasible sequential quadratic programming(FSQP) method.We do not employ standard least square approach.We divide the equations into two groups. One group, which contains the equations with zero residual,is treated as equality constraints. The square of other equations is regarded as objective function. Two groups are updated in every step.Therefore, the subproblem is updated at every step, which avoids the difficulty that it is required to lie in feasible region for FSQP.     

A globally convergent trust region algorithm for optimization with general constraints and simple bounds

1.IntroductionInthispaper,weconsiderthefollowingnonlinearprogr~ngproblemwherec(x)=(c,(x),c2(2),',We(.))',i(x)andci(x)(i=1,2,',m)arerealfunctions*ThisworkissupPOrtedbytheNationalNaturalScienceFOundationofChinaandtheManagement,DecisionandinformationSystemLab,theChineseAcademyofSciences.definedinD={xEReIISx5u}.Weassumethath相似文献   

不等式约束二次规划的一新算法

文献[1]提出了一般等式约束非线性规划问题一种求解途径．文献[2]应用这一途径给出了等式约束二次规划问题的一种算法，本文在文献[1]和[2]的基础上对不等式约束二次规划问题提出了一种新算法．     

非线性最优化一个超线收敛的可行下降算法

本文讨论非线性等式和不等式约束最优化的求解方法。首先将原问题扩充成一个只含不等式约束的参数规划，对于充分大的参数，扩充问题与原问题是等价的。然手建立具有以下特点的一个新算法。１）算法对扩充问题而言是可行下降的，参数只须自动调整有限次；２）每次迭代仅需解一个二次规划；３）在适当的假设下，算法超线性收敛于原问题的最优解。     

A GENERALIZED PROJECTION-SUCCESSIVE LINEAREQUATIONS ALGORITHM FOR NONLINEARLY EQUALITy AND INEQUALITY CONSTRAINED OPTIMIZATION AND ITS RATE OF CONVERGENCE

In this paper, a new superlinearly convergent algorithm is presented for optimization problems with general nonlineer equality and inequality Constraints, Comparing with other methods for these problems, the algorithm has two main advantages. First, it doesn‘t solve anyquadratic programming (QP), and its search directions are determined by the generalized projection technique and the solutions of two systems of linear equations. Second, the sequential points generated by the algoritbh satisfy all inequity constraints and its step-length is computed by the straight line search,The algorithm is proved to possesa global and auperlinear convergence.     

A new method of moving asymptotes for large-scale linearly equality-constrained minimization

A new method of moving asymptotes for large-scale minimization subject to linear equality constraints is discussed.In this method,linear equality constraints are deleted with null space technique and the descending direction is obtained by solving a convex separable subproblem of moving asymptotes in each iteration. New rules for controlling the asymptotes parameters are designed and the global convergence of the method under some reasonable conditions is established and proved.The numerical results show that the new method may be capable of processing some large scale problems.     

A result in surrogate duality for certain integer programming problems

We consider linear programming problems with some equality constraints. For such problems, surrogate relaxation formulations relaxing equality constraints existwith zero primal-dual gap both when all variables are restricted to be integers and when no variable is required to be integer. However, for such surrogate formulations, when the variables are mixed-integer, the primal-dual gap may not be zero. We establish this latter result by a counterexample.     

An improved sequential quadratic programming algorithm for solving general nonlinear programming problems

In this paper, a class of general nonlinear programming problems with inequality and equality constraints is discussed. Firstly, the original problem is transformed into an associated simpler equivalent problem with only inequality constraints. Then, inspired by the ideals of the sequential quadratic programming (SQP) method and the method of system of linear equations (SLE), a new type of SQP algorithm for solving the original problem is proposed. At each iteration, the search direction is generated by the combination of two directions, which are obtained by solving an always feasible quadratic programming (QP) subproblem and a SLE, respectively. Moreover, in order to overcome the Maratos effect, the higher-order correction direction is obtained by solving another SLE. The two SLEs have the same coefficient matrices, and we only need to solve the one of them after a finite number of iterations. By a new line search technique, the proposed algorithm possesses global and superlinear convergence under some suitable assumptions without the strict complementarity. Finally, some comparative numerical results are reported to show that the proposed algorithm is effective and promising.     

A Trust Region SQP Algorithm for Equality Constrained Parameter Estimation with Simple Parameter Bounds

We describe a new algorithm for a class of parameter estimation problems, which are either unconstrained or have only equality constraints and bounds on parameters. Due to the presence of unobservable variables, parameter estimation problems may have non-unique solutions for these variables. These can also lead to singular or ill-conditioned Hessians and this may be responsible for slow or non-convergence of nonlinear programming (NLP) algorithms used to solve these problems. For this reason, we need an algorithm that leads to strong descent and converges to a stationary point. Our algorithm is based on Successive Quadratic Programming (SQP) and constrains the SQP steps in a trust region for global convergence. We consider the second-order information in three ways: quasi-Newton updates, Gauss-Newton approximation, and exact second derivatives, and we compare their performance. Finally, we provide results of tests of our algorithm on various problems from the CUTE and COPS sets.