共查询到19条相似文献,搜索用时 156 毫秒
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本文利用指数型增广拉格朗日函数将一类广义半无限极大极小问题在一定条件下转化为标准的半无限极大极小问题,使它们具有相同的局部与全局最优解.我们给出了两个转化条件:一个是充分与必要条件,另一个是在实际中易于验证的充分条件.通过这种转化,我们给出了广义半无限极大极小问题的一个新的一阶最优性条件. 相似文献
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本文研究向量优化问题在严有效解意义下的最优性条件.在局部凸Hausdorff拓扑线性空间中.在近似锥一次类凸假设下,利用凸集分离定理得到了最优性必要条件.借助Gateaux导数引进了几种新的凸性,在新的凸性假设下得到了最优性充分条件. 相似文献
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Barbu等人在文[1]中时目标函数和约束算子都是Frechet可微的情况下证明了具有算子约束的数学规划的最优性必要条件.本文将这一问题推广为目标函数为非光滑的情形,给出了具有算子约束的Lipschitz规划的最优性充分条件和必要条件. 相似文献
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本文给出了拟可微优化的Fritz John必须条件与Shapiro最优性必要条件的等价性质以及两个最优性充分条件. 相似文献
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集值映射多目标规划的K-T最优性条件 总被引:18,自引:1,他引:17
讨论集值映射多目标规划(VP)的最优性条件问题.首先,在没有锥凹的假设下,利用集值映射的相依导数,得到了(VP)的锥--超有效解要满足的必要条件和充分条件.其次,在锥凹假设和比推广了的Slater规格更弱的条件下,给出了(VP)关于锥--超有效解的K--T型最优性必要条件和充分条件. 相似文献
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带约束的变尺度算法 总被引:3,自引:0,他引:3
田蔚文 《应用数学与计算数学学报》1992,6(1):42-45
迄今为止,变尺度算法是求解无约束最优化问题最有效的一类方法。因此,近年来,对约束最优化问题建立类似方法的工作。引起了许多优化工作者的兴趣,他们提出了Wilson-Han-Powell算法及其改进等等。并且证明在一定条件下,算法具有超线性的收敛率。但这些条件不仅要求很“高”,而且很难在计算前确定能否成立。文[4]利用文[1]和[2]的结果,提出一类新的算法,求解带线性等式约束条件的非线性规划问题。并且证明了算法的超线性收敛率。本文把这个结果推广到一般的约束规划问题: 相似文献
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In this paper, a new local optimization method for mixed integer quadratic programming problems with box constraints is presented by using its necessary global optimality conditions. Then a new global optimization method by combining its sufficient global optimality conditions and an auxiliary function is proposed. Some numerical examples are also presented to show that the proposed optimization methods for mixed integer quadratic programming problems with box constraints are very efficient and stable. 相似文献
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In this paper, we first establish some sufficient and some necessary global optimality conditions for quadratic integer programming
problems. Then we present a new local optimization method for quadratic integer programming problems according to its necessary
global optimality conditions. A new global optimization method is proposed by combining its sufficient global optimality conditions,
local optimization method and an auxiliary function. The numerical examples are also presented to show that the proposed optimization
methods for quadratic integer programming problems are very efficient and stable. 相似文献
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In this paper, we develop necessary conditions for global optimality that apply to non-linear programming problems with polynomial
constraints which cover a broad range of optimization problems that arise in applications of continuous as well as discrete
optimization. In particular, we show that our optimality conditions readily apply to problems where the objective function
is the difference of polynomial and convex functions over polynomial constraints, and to classes of fractional programming
problems. Our necessary conditions become also sufficient for global optimality for polynomial programming problems. Our approach
makes use of polynomial over-estimators and, a polynomial version of a theorem of the alternative which is a variant of the
Positivstellensatz in semi-algebraic geometry. We discuss numerical examples to illustrate the significance of our optimality
conditions. 相似文献
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In this paper we present necessary conditions for global optimality for polynomial problems with box or bivalent constraints using separable polynomial relaxations. We achieve this by first deriving a numerically checkable characterization of global optimality for separable polynomial problems with box as well as bivalent constraints. Our necessary optimality conditions can be numerically checked by solving semi-definite programming problems. Then, by employing separable polynomial under-estimators, we establish sufficient conditions for global optimality for classes of polynomial optimization problems with box or bivalent constraints. We construct underestimators using the sum of squares convex (SOS-convex) polynomials of real algebraic geometry. An important feature of SOS-convexity that is generally not shared by the standard convexity is that whether a polynomial is SOS-convex or not can be checked by solving a semidefinite programming problem. We illustrate the versatility of our optimality conditions by simple numerical examples. 相似文献
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H. Tuy 《Journal of Optimization Theory and Applications》2003,118(1):201-216
We discuss global optimality conditions and cutting plane algorithms for DC optimization. The discussion is motivated by certain incorrect results that have appeared recently in the literature on these topics. Incidentally, we investigate the relation of the Tikhonov reciprocity theorem to the optimality conditions for general nonconvex global optimization problems and show how the outer-approximation scheme developed earlier for DC programming can be used to solve a wider class of problems. 相似文献
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Z. Y. Wu J. Quan G. Q. Li J. Tian 《Journal of Optimization Theory and Applications》2012,153(2):408-435
Multivariate cubic polynomial optimization problems, as a special case of the general polynomial optimization, have a lot
of practical applications in real world. In this paper, some necessary local optimality conditions and some necessary global
optimality conditions for cubic polynomial optimization problems with mixed variables are established. Then some local optimization
methods, including weakly local optimization methods for general problems with mixed variables and strongly local optimization
methods for cubic polynomial optimization problems with mixed variables, are proposed by exploiting these necessary local
optimality conditions and necessary global optimality conditions. A global optimization method is proposed for cubic polynomial
optimization problems by combining these local optimization methods together with some auxiliary functions. Some numerical
examples are also given to illustrate that these approaches are very efficient. 相似文献
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Two approaches that solve the mixed-integer nonlinear bilevel programming problem to global optimality are introduced. The first addresses problems mixed-integer nonlinear in outer variables and C2-nonlinear in inner variables. The second adresses problems with general mixed-integer nonlinear functions in outer level. Inner level functions may be mixed-integer nonlinear in outer variables, linear, polynomial, or multilinear in inner integer variables, and linear in inner continuous variables. This second approach is based on reformulating the mixed-integer inner problem as continuous via its vertex polyheral convex hull representation and solving the resulting nonlinear bilevel optimization problem by a novel deterministic global optimization framework. Computational studies illustrate proposed approaches. 相似文献
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In this paper, we present Lagrange multiplier necessary conditions for global optimality that apply to non-convex optimization
problems beyond quadratic optimization problems subject to a single quadratic constraint. In particular, we show that our
optimality conditions apply to problems where the objective function is the difference of quadratic and convex functions over
a quadratic constraint, and to certain class of fractional programming problems. Our necessary conditions become necessary
and sufficient conditions for global optimality for quadratic minimization subject to quadratic constraint. As an application,
we also obtain global optimality conditions for a class of trust-region problems. Our approach makes use of outer-estimators,
and the powerful S-lemma which has played key role in control theory and semidefinite optimization. We discuss numerical examples
to illustrate the significance of our optimality conditions.
The authors are grateful to the referees for their useful comments which have contributed to the final preparation of the
paper. 相似文献