非线性半定规划的逐次线性化柔性惩罚法

针对非线性不等式约束半定规划问题提出一种新的逐次线性化方法, 新算法既不要求罚函数单调下降, 也不使用过滤技巧, 尝试步的接受准则仅仅依赖于目标函数和约束违反度, 罚函数中对应于成功迭代点的罚因子不需要单调增加. 新算法或者要求违反约束度量有足够改善, 或者在约束违反度的一个合理范围内要求目标函数值充分下降, 在通常假设条件下, 分析了新算法的适定性及全局收敛性. 最后, 给出了非线性半定规划问题的数值试验结果, 结果表明了新算法的有效性.     

非线性半定规划的逐次线性化柔性惩罚法（英文）

针对非线性不等式约束半定规划问题提出一种新的逐次线性化方法,新算法既不要求罚函数单调下降,也不使用过滤技巧,尝试步的接受准则仅仅依赖于目标函数和约束违反度,罚函数中对应于成功迭代点的罚因子不需要单调增加.新算法或者要求违反约束度量有足够改善,或者在约束违反度的一个合理范围内要求目标函数值充分下降,在通常假设条件下,分析了新算法的适定性及全局收敛性.最后,给出了非线性半定规划问题的数值试验结果,结果表明了新算法的有效性.     

一个修正的罚函数方法

本文通过给出的一个修正的罚函数,把约束非线性规划问题转化为无约束非线性规划问题.我们讨论了原问题与相应的罚问题局部最优解和全局最优解之间的关系,并给出了乘子参数和罚参数与迭代点之间的关系,最后给出了一个简单算法,数值试验表明算法是有效的.     

一类非线性三层规划问题的罚函数方法

文章研究了一类结构为非线性-线性-线性三:层规划问题的求解方法.首先,基于下层问题的Karush-Kuhn-Tucker (K-K-T)最优性条件,将该类非线性三层规划问题转化为具有互补约束的非线性二层规划,同时将下层问题的互补约束作为罚项添加到上层目标;然后,再次利用下层问题的K-K-T最优性条件将非线性二层规划转化为非线性单层规划,并再次将得到的互补约束作为上层目标的罚项,构造了该类非线性三层规划问题的罚问题.通过对罚问题性质的分析,得到了该类非线性三层规划问题最优解的必要条件,并设计了罚函数算法.数值结果表明所设计的罚函数算法是可行、有效的.     

不等式约束优化问题的低阶精确罚函数的光滑化算法

对不等式约束优化问题提出了一个低阶精确罚函数的光滑化算法. 首先给出了光滑罚问题、非光滑罚问题及原问题的目标函数值之间的误差估计,进而在弱的假
设之下证明了光滑罚问题的全局最优解是原问题的近似全局最优解. 最后给出了一个基于光滑罚函数的求解原问题的算法,证明了算法的收敛性,并给出数值算例说明算法的可行性.     

一种双层规划的光滑化目标罚函数算法

论文研究了一种双层规划的光滑化目标罚函数算法,在一些条件下,证明了光滑化罚优化问题等价于原双层规划问题,而且,当下层规划问题是凸规划问题时, 给出了一个求解算法和收敛性证明.     

一类弱线性二层多目标规划的罚函数方法

本文研究了一类线性二层多目标规划(上层为单目标、下层为多目标)"悲观最优解"的求解问题.利用罚函数方法给出了该类问题"悲观最优解"的存在性定理,证明了罚函数的精确性,同时设计了相应的罚函数算法.数值结果表明所设计的罚函数方法是可行的.     

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     

一种双层规划的光滑化目标罚函数算法（英文）

论文研究了一种双层规划的光滑化目标罚函数算法,在一些条件下,证明了光滑化罚优化问题等价于原双层规划问题,而且,当下层规划问题是凸规划问题时,给出了一个求解算法和收敛性证明.     

求解非线性规划问题的一类对偶算法

本文提出了一类求解不等式约束非线性规划问题的构造性对偶算法,我们证明在适当的条件下,势函数的罚参数存在一个阀值,当罚参数小于这个阀值时,由这一方法所产生的序列局部收敛于问题的一个Kuhn-Tucker解,我们也建立了解的依赖于罚参数的误差上界,最后,我们给出了一个特残势函数的数值结果。     

遗传算法求解约束非线性规划及Matlab实现

对于约束非线性规划问题,传统的方法:可行方向法、惩罚函数法计算烦琐且精度不高.用新兴的遗传算法来解决约束非线性规划,核心是惩罚函数的构造.以前的惩罚函数遗传算法有的精度较低,有的过于复杂.本文在两个定义的基础上构造了新的惩罚函数,并在新的惩罚函数的基础上,提出了一种解决约束非线性最优化问题的方法.通过两个例子应用Matlab说明了这个算法的可行性.     

Algorithm of Barrier Objective Penalty Function

In this paper, an algorithm of barrier objective penalty function for inequality constrained optimization is studied and a conception–the stability of barrier objective penalty function is presented. It is proved that an approximate optimal solution may be obtained by solving a barrier objective penalty function for inequality constrained optimization problem when the barrier objective penalty function is stable. Under some conditions, the stability of barrier objective penalty function is proved for convex programming. Specially, the logarithmic barrier function of convex programming is stable. Based on the barrier objective penalty function, an algorithm is developed for finding an approximate optimal solution to an inequality constrained optimization problem and its convergence is also proved under some conditions. Finally, numerical experiments show that the barrier objective penalty function algorithm has better convergence than the classical barrier function algorithm.     

Convergence of an Interior Point Algorithm for Continuous Minimax

We propose an algorithm for the constrained continuous minimax problem. The algorithm uses a quasi-Newton search direction, based on subgradient information, conditional on maximizers. The initial problem is transformed to an equivalent equality constrained problem, where the logarithmic barrier function is used to ensure feasibility. In the case of multiple maximizers, the algorithm adopts semi-infinite programming iterations toward epiconvergence. Satisfaction of the equality constraints is ensured by an adaptive quadratic penalty function. The algorithm is augmented by a discrete minimax procedure to compute the semi-infinite programming steps and ensure overall progress when required by the adaptive penalty procedure. Progress toward the solution is maintained using merit functions.     

一个解非线性0-1整数规划问题基于罚函数的混合粒子群优化算法

利用罚函数思想把非线性0-1整数规划问题转化为无约束最优化问题,然后把粒子群优化和罚函数方法结合构造出一个基于罚函数的混合粒子群优化算法,数值结果表明所提出的算法是有效的.     

A Continuation Algorithm for Max-Cut Problem

A continuation algorithm for the solution of max-cut problems is proposed in this paper. Unlike the available semi-definite relaxation, a max-cut problem is converted into a continuous nonlinear programming by employing NCP functions, and the resulting nonlinear programming problem is then solved by using the augmented Lagrange penalty function method. The convergence property of the proposed algorithm is studied. Numerical experiments and comparisons with the Geomeans and Williamson randomized algorithm made on some max-cut test problems show that the algorithm generates satisfactory solutions for all the test problems with much less computation costs.     

A primal–dual augmented Lagrangian penalty-interior-point filter line search algorithm

Interior-point methods have been shown to be very efficient for large-scale nonlinear programming. The combination with penalty methods increases their robustness due to the regularization of the constraints caused by the penalty term. In this paper a primal–dual penalty-interior-point algorithm is proposed, that is based on an augmented Lagrangian approach with an \(\ell 2\)-exact penalty function. Global convergence is maintained by a combination of a merit function and a filter approach. Unlike the majority of filter methods, no separate feasibility restoration phase is required. The algorithm has been implemented within the solver WORHP to study different penalty and line search options and to compare its numerical performance to two other state-of-the-art nonlinear programming algorithms, the interior-point method IPOPT and the sequential quadratic programming method of WORHP.     

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.     

A column generation algorithm for nonlinear programming

An algorithm using column generation and penalty function techniques is presented. A linear program with a uniformly bounded number of columns, similar to the restricted master in generalized programming, is used to reduce the number of constraints included in forming a penalty function. The penalty function is used as a Lagrangian in an unconstrained subproblem.This work was supported in part by National Science Foundation Grant GS-3032.     

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.     

A two-parameter exact penalty function for nonlinear programming

A sequential quadratic programming algorithm for nonlinear programs using anl -exact penalty function is described. Numerical results are also presented. These results show that the algorithm is competitive with other exact penalty function based algorithms and that the inclusion of the second penalty parameter can be advantageous.