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．     

某类等式约束二次规划问题的一个共轭方向法

本文提出了一种求解某类等式约束二次规划问题的一个共轭方向迭代法，并给出了算法的有限终止性证明．同时我们把此算法推广到不等式约束二次规划问题中，从而得到了一种求解不等式约束二次规划问题的算法．     

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．     

不等式约束优化一个新的SQP算法

本文提出了一个处理不等式约束优化问题的新的SQP算法．和传统的SQP算法相比，该算法每步只需求解一个仅含等式约束的子二次规划，从而减少了算法的计算工作量．在适当的条件下，证明算法是全局收敛的且具有超线性收敛速度．数值实验表明算法是有效的．     

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．     

用非线性方程组求解等式约束非线性规划问题的降维算法

本文研究线性和非线性等式约束非线性规划问题的降维算法.首先,利用一般等式约束问题的降维方法,将线性等式约束非线性规划问题转换成一个非线性方程组,解非线性方程组即得其解;然后,对线性和非线性等式约束非线性规划问题用Lagrange乘子法,将非线性约束部分和目标函数构成增广的Lagrange函数,并保留线性等式约束,这样便得到一个线性等式约束非线性规划序列,从而,又将问题转化为求解只含线性等式约束的非线性规划问题.     

一种基于LVI求解二次规划问题的数值算法

给出并研究了一种数值算法(简称94LVI算法),用于求解带等式和双端约束的二次规划问题. 这类带约束的二次规划问题首先被转换为线性变分不等式问题,该问题等价于分段线性投影等式.接着使用94LVI算法求解上述分段线性投影等式,从而得到QP问题的最优解. 进一步给出了94LVI算法的全局收敛性证明. 94LVI算法与经典有效集算法的对比实验结果证实了给出的94LVI算法在求解二次规划问题上的高效性与优越性.     

不等式约束优化基于新型积极识别集的SQCQP算法

本文提出一个新的求解非线性不等式约束优化问题的罚函数型序列二次约束二次规划(SQCQP)算法.算法每次迭代只需求解一个凸二次约束二次规划(QCQP)子问题,且通过引入新型积极识别集技术,QCQP子问题的规模显著减小,从而降低计算成本.在不需要函数凸性等较弱假设下,算法具有全局收敛性.初步的数值试验表明算法是稳定有效的.     

一个求解箱约束二次规划的非内点预估校正算法

利用Chen-Harker-Kanzow-Smale光滑技术,给出了一个求解箱约束二次规划的预估校正的算法,它是Xu‘s方程的进一步研究,它的思想是将问题的K-T条件转化成一组光滑的等式,再用预估校正方法求解.同现存的算法相比,该算法具有较快的收敛速度,且所需的条件相对较弱.本文改进了该领域内的一些最新结果.     

一般约束优化基于识别函数的模松弛算法

借助于半罚函数和产生工作集的识别函数以及模松弛SQP算法思想, 本文建立了求解带等式及不等式约束优化的一个新算法. 每次迭代中, 算法的搜索方向由一个简化的二次规划子问题及一个简化的线性方程组产生. 算法在不包含严格互补性的温和条件下具有全局收敛性和超线性收敛性. 最后给出了算法初步的数值试验报告.     

A feasible SQP method for nonlinear programming

In this paper, a new SQP algorithm is presented to solve the general nonlinear programs with mixed equality and inequality constraints. Quoted from P. Spellucci (see [9]), this method maybe be named sequential equality constrained quadratic programming (SECQP) algorithm. Per single iteration, based on an active set strategy ( see [9]), this SECQP algorithm requires only to solve equality constrained quadratic programming subproblems or system of linear equations. The theoretical analysis shows that global and superlinear convergence can be induced under some suitable conditions.     

A Quasi-Newton Quadratic Penalty Method for Minimization Subject to Nonlinear Equality Constraints

We present a modified quadratic penalty function method for equality constrained optimization problems. The pivotal feature of our algorithm is that at every iterate we invoke a special change of variables to improve the ability of the algorithm to follow the constraint level sets. This change of variables gives rise to a suitable block diagonal approximation to the Hessian which is then used to construct a quasi-Newton method. We show that the complete algorithm is globally convergent. Preliminary computational results are reported.     

A quadratically approximate framework for constrained optimization,global and local convergence

This paper presents a quadratically approximate algorithm framework （QAAF） for solving general constrained optimization problems, which solves, at each iteration, a subproblem with quadratic objective function and quadratic equality together with inequality constraints. The global convergence of the algorithm framework is presented under the Mangasarian-Fromovitz constraint qualification （MFCQ）, and the conditions for superlinear and quadratic convergence of the algorithm framework are given under the MFCQ, the constant rank constraint qualification （CRCQ） as well as the strong second-order sufficiency conditions （SSOSC）. As an incidental result, the definition of an approximate KKT point is brought forward, and the global convergence of a sequence of approximate KKT points is analysed.     

Feasible Direction Interior-Point Technique for Nonlinear Optimization

We propose a feasible direction approach for the minimization by interior-point algorithms of a smooth function under smooth equality and inequality constraints. It consists of the iterative solution in the primal and dual variables of the Karush–Kuhn–Tucker first-order optimality conditions. At each iteration, a descent direction is defined by solving a linear system. In a second stage, the linear system is perturbed so as to deflect the descent direction and obtain a feasible descent direction. A line search is then performed to get a new interior point and ensure global convergence. Based on this approach, first-order, Newton, and quasi-Newton algorithms can be obtained. To introduce the method, we consider first the inequality constrained problem and present a globally convergent basic algorithm. Particular first-order and quasi-Newton versions of this algorithm are also stated. Then, equality constraints are included. This method, which is simple to code, does not require the solution of quadratic programs and it is neither a penalty method nor a barrier method. Several practical applications and numerical results show that our method is strong and efficient.     

An Interior Point Algorithm for Computing Saddle Points of Constrained Continuous Minimax

The aim of this paper is to present an algorithm for finding a saddle point to the constrained minimax problem. The initial problem is transformed into an equivalent equality constrained problem, and then the interior point approach is used. To satisfy the original inequality constraints a logarithmic barrier function is used and special care is given to step size parameter to keep the variables within permitted boundaries. Numerical results illustrating the method are given.     

Sequential quadratically constrained quadratic programming norm-relaxed algorithm of strongly sub-feasible directions

In this paper, we present a sequential quadratically constrained quadratic programming (SQCQP) norm-relaxed algorithm of strongly sub-feasible directions for the solution of inequality constrained optimization problems. By introducing a new unified line search and making use of the idea of strongly sub-feasible direction method, the proposed algorithm can well combine the phase of finding a feasible point (by finite iterations) and the phase of a feasible descent norm-relaxed SQCQP algorithm. Moreover, the former phase can preserve the “sub-feasibility” of the current iteration, and control the increase of the objective function. At each iteration, only a consistent convex quadratically constrained quadratic programming problem needs to be solved to obtain a search direction. Without any other correctional directions, the global, superlinear and a certain quadratic convergence (which is between 1-step and 2-step quadratic convergence) properties are proved under reasonable assumptions. Finally, some preliminary numerical results show that the proposed algorithm is also encouraging.     

解等式约束优化的既约Hessian依赖域方法

本文提出了解等式约束优化的一个信赖域方法,该方法以既约Hessian逐步二次规划为基础,它享有信赖域方法与既约Hessian方法的优点,在通常条件下,证明了算法的全局收敛性。     

约束最优化的一个使用非单调线搜索的超线性收敛算法

Abstract. In the paper, a new mixed algorithm combined with schemes of nonmonotone line search, the systems of linear equations for higher order modification and sequential quadratic programming for constrained optimizations is presented. Under some weaker assumptions,without strict complementary condition, the algorithm is globally and superlinearly convergent.     

A working set SQCQP algorithm with simple nonmonotone penalty parameters

In this paper, we present a new sequential quadratically constrained quadratic programming (SQCQP) algorithm, in which a simple updating strategy of the penalty parameter is adopted. This strategy generates nonmonotone penalty parameters at early iterations and only uses the multiplier corresponding to the bound constraint of the quadratically constrained quadratic programming (QCQP) subproblem instead of the multipliers of the quadratic constraints, which will bring some numerical advantages. Furthermore, by using the working set technique, we remove the constraints of the QCQP subproblem that are locally irrelevant, and thus the computational cost could be reduced. Without assuming the convexity of the objective function or the constraints, the algorithm is proved to be globally, superlinearly and quadratically convergent. Preliminary numerical results show that the proposed algorithm is very promising when compared with the tested SQP algorithms.