战斗对策:有约束极小极大途径(Ⅰ)(英文)

本文把战斗对策归结为有约束极小极大问题,讨论解的存在性．引进不连续罚函数后,把有约束问题化为无约束极小极大问题．     

战斗对策:有约束极小极大途径(Ⅱ)

本文提出几个用集合,测度和积分工具来的极小极大判别准则,用来解有约束极小极大问题．     

一类极大极小问题的模型转化及算法

本通过辅助规划和Lagrange对偶，把带等式和不等式约束的极大极小问题转化为带线性约束的凸规划问题，给出了一个信赖域方法，并证明了方法的可行性。     

一般约束极大极小问题的一个有效的近似解法

一般约束极大极小问题的一个有效的近似解法唐焕文，张立卫，王云诚（大连理工大学应用数学系，辽宁，１１６０２４）．摘要＊从共扼的观点出发，导出了极大熵函数，给出了处理一般约束极大极小问题的一个有效的近似方法—极大熵方法，并在较弱的条件下，证明了算法的收敛...     

精确罚函数和极小极大问题

在这篇文章中我们研究了对于不等式约束的非线性规划问题如何根据极小极大问题的鞍点来找精确罚问题的解。对于一个具有不等式约束的非线性规划问题,通过罚函数,我们构造出一个极小极大问题,应用交换“极小”或“极大”次序的策略,证明了罚问题的鞍点定理。研究结果显示极小极大问题的鞍点是精确罚问题的解。     

极小扰动约束非线性规划的最优性条件

考虑当目标函数在约束条件下的最优值作扰动时，使各约束作极小扰动的非线性规划问题．文中引进了极小扰动约束规划的极小扰动有效解概念．利用把问题归为一个相应的多目标规划问题，给出了极小扰动约束有效解的最优性条件．     

一种新的求解带约束的有限极大极小问题的精确罚函数

提出了一种新的精确光滑罚函数求解带约束的极大极小问题．仅仅添加一个额外的变量,利用这个精确光滑罚函数,将带约束的极大极小问题转化为无约束优化问题． 证明了在合理的假设条件下,当罚参数充分大,罚问题的极小值点就是原问题的极小值点．进一步,研究了局部精确性质．数值结果表明这种罚函数算法是求解带约束有限极大极小问题的一种有效算法．     

求解约束极小极大问题的一种K─S函数的近似迭代法

借助于极大熵方法和逼近法，给出了一种求解约束极小极大问题的K－S函数近似迭代法，同时讨论算法的有关收敛性．     

极大熵方法与二次规划子问题的显式解

本文对混合约束极大极小问题的目标函数与约束分别用熵函数来逼近,讨论了逼近问题的二次规划子问题的搜索方向的显式形式,并给出了极大极小问题和多目标规划的二次规划予问题的显式解。将所得结果用于相应的算法中,可提高算法的有效性。     

非凸广义半无限极大极小问题的全局收敛方法

1 引言广义极大极小问题在工程优化设计、电子线路优化设计、计算机辅助设计及最优控制中有着广泛的应用．由于广义极大极小问题是一类拟可微问题,所以我们可以采用针对拟可微函数的算法来求解,见文[4]．另外,在一定条件下,广义有限极大极小问题还可以转化为光滑约束的非线性规划问题[3]．但到目前为止,大多数算法仅考虑广义有限极大     

A constrained independent set problem for matroids

In this note, we study a constrained independent set problem for matroids. The problem can be regarded as an ordered version of the matroid parity problem. By a reduction of this problem to matroid intersection, we prove a min-max formula. We show how earlier results of Hefner and Kleinschmidt on the so-called MS-matchings fit in our framework.     

Generalized Semi-Infinite Programming: Optimality Conditions Involving Reverse Convex Problems

This article deals with a generalized semi-infinite programming problem (S). Under appropriate assumptions, for such a problem we give necessary and sufficient optimality conditions via reverse convex problems. In particular, a necessary and sufficient optimality condition reduces the problem (S) to a min-max problem constrained with compact convex linked constraints.     

Constrained ratio games and generalized fractional programming

A certain constrained ratio game is shown to be equivalent to a pair of mutually dual generalized fractional programming problems. This also extends the concept of symmetric duality to min-max fractional programming.Research by this author was carried out while he was visiting I.I.T. Delhi, India, under an Australian Vice-Chancellors' Committee Visiting Fellowship.     

Prediction-correction alternating direction method for a class of constrained min-max problems

The problems concerned in this paper are a class of constrained min-max problems. By introducing the Lagrange multipliers to the linear constraints, such problems can be solved by some projection type prediction-correction methods. However, to obtain components of the predictor one by one, we use an alternating direction method. And then the new iterate is generated by a minor correction. Global convergence of the proposed method is proved. Finally, numerical results for a constrained single-facility location problem are provided to verify that the new method is effective for some practical problems.      

Min-max control of systems approximated by simple models:L 1-Type cost functionals

A control problem for actual processes, modeled by simple dynamic linear systems, is studied. A min-max approach is taken, since the problem is reduced to the control of a model, whose output is affected by an input-dependent signal constrained in norm.Particular attention is given to the features of the penalty functional, since it is desired to synthesize the min-max control by means of a feedback on the states of the model; for example, a quadratic functional does not have this property. AnL ₁-type functional is then proposed, which is not differentiable; by means of duality techniques, however, the minimization can be carried out. The min-max is obtained both by iterative algorithms, both as a function of the actual value of the model state: this function is the solution of a set of partial differential equations.This work was supported by the CENS and the Gruppo Nazionale per l'Analisi Funzionale e le sue Applicazioni, Consiglio Nazionale delle Ricerche (CNR), Roma, Italy.     

Solvability Criterion for the Constrained Discrete Lyapunov and Riccati Equations

Conditions for the solvability of the discrete Lyapunov and the discrete Riccati equations subject to linear equality constraints are derived. These problems arise naturally in the context of output min-max robust control. It is shown that the following problems are equivalent to one another: (a) the solvability of the constrained discrete Riccati equation; and (b) the existence of a feedback gain that guarantees the solvability of the constrained discrete Lyapunov equation of the resulting closed loop. A simple criterion for the existence of a solution to both problems is presented. These problems are shown to be related to the discrete positive real property.     

基于参数李雅普诺夫函数的鲁棒预测控制器

针对多包描述的不确定系统,提出一种新的鲁棒约束预测控制器.离线设计时引入参数Lyapunov函数以减少单一Lyapunov函数设计时的保守性,得到多包系统Worst-case情况下性能最优的不变集,在线求解多包系统无穷时域性能指标的min-max优化问题.设计采用了时变的终端约束集,扩大了初始可行域,而且能够获得较优的控制性能.仿真结果验证了该方法的有效性.