Along with the development of minimax theory , it had been applied in game theory , mathematical economics , optimization theory , variational inequalities , fixed - point theory , potential theory , section problem , etc 随着极大极小理论的发展，它已经应用于博弈论，数量经济学，最优化理论，变分不等式，微分方程，不动点理论，位势论，截面问题等诸多领域。
As applications , some minimax inequalities and saddle point the - orems , fixed point theorems and section theorems , maximal element theorems and the existence theorems of equilibrium for abstract economies are obtained in l - convex spaces 作为应用，我们得到了新的极大极小不等式、鞍点定理、不动点定理、截口定理和极大元定理，并研究了抽象经济的平衡存在性。
In this thesis , we extend the entropy regularization method in two ways : from the min - max problem to general inequality constrained optimization problems and from the entropy function to more general functions 本文从两个方面发展了这种熵正则化方法，即将其从极大极小问题推广到一般不等式约束优化问题上和用一般函数代替熵函数作正则项，建立新的正则化方法。
In chapter one , r - kkm mappings is discussed . the more general generalized l - r - kkm theorems are established in l - convex space . as applications , a minimax inequalities and a saddle point theorem are obtained in noncompact l - convex spaces 章中，研究了r - kkm映像，在l -凸空间中得到了更为一般的广义l - r - kkm型定理，给出了对极大极小不等式和鞍点存在问题的应用。
This dissertation studies mainly theories and according numerical implementation of a class of dual algorithms for nonlinear optimization problems , including unconstrained minimax problems and constrained nonlinear programming problems 本文主要研究非线性优化中的一类对偶算法，包括无约束极大极小问题的对偶算法和约束非线性规划问题的一类对偶算法的理论与相应的数值实现。
We apply these dual algorithms to solve a large number of nonlinear optimization problems with relative small scale , including inequality constrained optimization problems , unconstrained minimax problems and general constrained optimization problems 用这些算法计算大量的规模不是很大的不等式约束优化问题，无约束极大极小问题，一般约束优化问题，数值结果表明它们是有效的
In the present paper , a max - min theorem and a max theorem are proved on local convex topological linear spaces , as an application , it is obtained that there exists optimal mixed strategies in a two - person game with an infinite pure strategy set 摘要证明了局部凸线性拓扑空间上实值连续泛函的极大极小定理与极大定理，并由此证明了一类具有无限纯策略集的二人对策中最优混合策略的存在性。
Then the perturbation methods are used to an equivalent nlp problem of minmax problems and the resulted smooth functions are just aggregate functions obtained by maximum entropy principle and minimum cross - entropy principle , respectively 然后文中把这种方法应用到有限维极大极小问题的一个等价非线性规划问题，得到了相应的光滑函数，且与用最大熵原则和最小叉熵原则得到的凝聚函数相同。
The module conversion for a kind of max - min problems is given , namely , the max - min problem with equality and inequality constraint is converted into convex problem with linear constraint , which provides theoretical basis for designing effective algorithms 最后，给出一类极大极小问题的模型转化，把带等式、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，这为设计更为有效的算法提供了理论依据。
Maximum entropy method is an effective smoothing one for the finite min - max problem , which , by adding shannon ' s informational entropy as a regularizing term to the lagrangian function of min - max problem , yields a smooth function that uniformly approaches the non - smooth max - valued function 极大熵方法是解有限极大极小问题的一种有效光滑化法，它通过在极大极小问题的拉格朗日函数上引进shannon信息熵作正则项，给出一致逼近极大值函数的光滑函数。
