共查询到19条相似文献,搜索用时 156 毫秒
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《数学物理学报(A辑)》2020,(1)
利用共轭函数的上图性质,引入新的约束规范条件,等价刻画了目标函数为凸函数与凸复合函数之和的复合优化问题及其Fenchel-Lagrange对偶问题之间的强对偶与稳定强对偶. 相似文献
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近似锥-次类凸集值优化的严有效性 总被引:16,自引:0,他引:16
在Hausdorff局部凸拓扑线性空间中考虑约束集值优化问题(VP)的严有效性.在近似锥-次类凸假设下,利用凸集分离定理,分别得到了Kuhn-Tucker型和Lagrange型最优性条件,建立了与(VP)等价的两种形式的无约束优化. 相似文献
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算子D~α及其刻划的亚纯p叶函数类 总被引:1,自引:0,他引:1
用算子Dα刻划了亚纯星象函数,亚纯凸象函数,亚纯近于凸函数和亚纯拟凸函数的新子类,建立了包含关系,讨论了这些类中函数积分算子的性质. 相似文献
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The finite-dimensional problems of outer and inner estimation of a convex compact set by a ball of some norm (circumscribed and inscribed ball problems) are considered. The stability of the solution with respect to the error in the specification of the estimated compact set is generally characterized. A new solution criterion for the outer estimation problem is obtained that relates the latter to the inner estimation problem for the lower Lebesgue set of the distance function to the most distant point of the estimated compact set. A quantitative estimate for the stability of the center of an inscribed ball is given under the additional assumption that the compact set is strongly convex. Assuming that the used norm is strongly quasi-convex, a quantitative stability estimate is obtained for the center of a circumscribed ball. 相似文献
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Juan Enrique Martínez-Legaz José Vicente-Pérez 《Journal of Mathematical Analysis and Applications》2011,376(2):602-612
A subset of a locally convex space is called e-convex if it is the intersection of a family of open halfspaces. An extended real-valued function on such a space is called e-convex if its epigraph is e-convex. In this paper we introduce a suitable support function for e-convex sets as well as a conjugation scheme for e-convex functions. 相似文献
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Generalized polyhedral convex sets, generalized polyhedral convex functions on locally convex Hausdorff topological vector spaces, and the related constructions such as sum of sets, sum of functions, directional derivative, infimal convolution, normal cone, conjugate function, subdifferential are studied thoroughly in this paper. Among other things, we show how a generalized polyhedral convex set can be characterized through the finiteness of the number of its faces. In addition, it is proved that the infimal convolution of a generalized polyhedral convex function and a polyhedral convex function is a polyhedral convex function. The obtained results can be applied to scalar optimization problems described by generalized polyhedral convex sets and generalized polyhedral convex functions. 相似文献
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Wiesława T. Obuchowska 《Computational Optimization and Applications》2006,33(2-3):349-364
In this paper we are concerned with the problem of boundedness and the existence of optimal solutions to the constrained optimization
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We present necessary and sufficient conditions for boundedness of either a faithfully convex or a quasi-convex polynomial
function over the feasible set defined by a system of faithfully convex inequality constraints and/or quasi-convex polynomial
inequalities, where the faithfully convex functions satisfy some mild assumption. The conditions are provided in the form
of an algorithm, terminating after a finite number of iterations, the implementation of which requires the identification
of implicit equality constraints in a homogeneous linear system. We prove that the optimal solution set of the considered
problem is nonempty, this way extending the attainability result well known as the so-called Frank-Wolfe theorem. Finally
we show that our extension of the Frank-Wolfe theorem immediately implies continuity of the solution set defined by the considered
system of (quasi)convex inequalities. 相似文献
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P. Coutat M. Volle J. E. Martinez-Legaz 《Journal of Optimization Theory and Applications》1996,88(2):365-379
Convex functions with continuous epigraph in the sense of Gale and Klée have been studied recently by Auslender and Coutat in a finite-dimensional setting. Here, we provide characterizations of such functionals in terms of the Legendre-Fenchel transformation in general locally convex spaces. Also, we show that the concept of continuous convex sets is of interest in these spaces. We end with a characterization of convex functions on Euclidean spaces with continuous level sets. 相似文献
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In this paper we consider optimization problems defined by a quadratic objective function and a finite number of quadratic inequality constraints. Given that the objective function is bounded over the feasible set, we present a comprehensive study of the conditions under which the optimal solution set is nonempty, thus extending the so-called Frank-Wolfe theorem. In particular, we first prove a general continuity result for the solution set defined by a system of convex quadratic inequalities. This result implies immediately that the optimal solution set of the aforementioned problem is nonempty when all the quadratic functions involved are convex. In the absence of the convexity of the objective function, we give examples showing that the optimal solution set may be empty either when there are two or more convex quadratic constraints, or when the Hessian of the objective function has two or more negative eigenvalues. In the case when there exists only one convex quadratic inequality constraint (together with other linear constraints), or when the constraint functions are all convex quadratic and the objective function is quasi-convex (thus allowing one negative eigenvalue in its Hessian matrix), we prove that the optimal solution set is nonempty. 相似文献
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G. E. Ivanov 《Mathematical Notes》2006,79(1-2):55-78
In this paper, the notion of a weakly convex set is introduced. Sharp estimates for the weak convexity constants of the sum and difference of such sets are given. It is proved that, in Hilbert space, the smoothness of a set is equivalent to the weak convexity of the set and its complement. Here, by definition, the smoothness of a set means that the field of unit outward normal vectors is defined on the boundary of the set; this vector field satisfies the Lipschitz condition. We obtain the minimax theorem for a class of problems with smooth Lebesgue sets of the goal function and strongly convex constraints. As an application of the results obtained, we prove the alternative theorem for program strategies in a linear differential quality game. 相似文献
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本文证明了赋范线性空间中闭弱拟凸集必为凸集,并指出郭元明的”弱拟凸集的一些性质及其应用”、“广义凸集的联合逼近特性”两文中的主要结论实质上是已知的结果. 相似文献