首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到10条相似文献,搜索用时 140 毫秒
1.
The concepts of L-convex function and M-convex function have recently been introduced by Murota as generalizations of submodular function and base polyhedron, respectively, and discrete separation theorems are established for L-convex/concave functions and for M-convex/concave functions as generalizations of Frank’s discrete separation theorem for submodular/supermodular set functions and Edmonds’ matroid intersection theorem. This paper shows the equivalence between Murota’s L-convex functions and Favati and Tardella’s submodular integrally convex functions, and also gives alternative proofs of the separation theorems that provide a geometric insight by relating them to the ordinary separation theorem in convex analysis. Received: November 27, 1997 / Accepted: December 16, 1999?Published online May 12, 2000  相似文献   

2.
In this paper, by virtue of the epigraph technique, we first introduce some new regularity conditions and then obtain some complete characterizations of the Fenchel–Lagrange duality and the stable Fenchel–Lagrange duality for a new class of DC optimization involving a composite function. Moreover, we apply the strong and stable strong duality results to obtain some extended (stable) Farkas lemmas and (stable) alternative type theorems for this DC optimization problem. As applications, we obtain the corresponding results for a composed convex optimization problem, a DC optimization problem, and a convex optimization problem with a linear operator, respectively.  相似文献   

3.
4.
熵正则化方法与指数(乘子)罚函数法之间的关系   总被引:1,自引:0,他引:1  
由于极大极小问题在许多科学与工程中有着重要应用,特别是形如max的函数频繁地出现在各类数值分析和优化问题中,因此对于求解该类问题的算法研究长久不衰,这些算法一般分为两大类:一类是直接法,其算法设计仅以有效地求解原问题(P)为目的;另一类是间接法,其算法以找一个能够替代不可微max函数φ(x)的光滑函数为目的,故这类算法被称为光滑化方法,文[1,2]中的熵正则化方法就属于光滑化方法范畴。  相似文献   

5.
This paper presents a canonical duality theory for solving quadratic minimization problems subjected to either box or integer constraints. Results show that under Gao and Strang’s general global optimality condition, these well-known nonconvex and discrete problems can be converted into smooth concave maximization dual problems over closed convex feasible spaces without duality gap, and can be solved by well-developed optimization methods. Both existence and uniqueness of these canonical dual solutions are presented. Based on a second-order canonical dual perturbation, the discrete integer programming problem is equivalent to a continuous unconstrained Lipschitzian optimization problem, which can be solved by certain deterministic technique. Particularly, an analytical solution is obtained under certain condition. A fourth-order canonical dual perturbation algorithm is presented and applications are illustrated. Finally, implication of the canonical duality theory for the popular semi-definite programming method is revealed.  相似文献   

6.
M. D. Fajardo  J. Vidal 《Optimization》2016,65(9):1675-1691
By means of a conjugation scheme based on generalized convex conjugation theory instead of Fenchel conjugation, we build an alternative dual problem, using the perturbational approach, for a general optimization one defined on a separated locally convex topological space. Conditions guaranteeing strong duality for primal problems which are perturbed by continuous linear functionals and their respective dual problems, which is named stable strong duality, are established. In these conditions, the fact that the perturbation function is evenly convex will play a fundamental role. Stable strong duality will also be studied in particular for Fenchel and Lagrange primal–dual problems, obtaining a characterization for Fenchel case.  相似文献   

7.
The paper is devoted to the study of a new class of conic constrained optimization problems with objectives given as differences of a composite function and a convex function. We first introduce some new notions of constraint qualifications in terms of the epigraphs of the conjugates of these functions. Under the new constraint qualifications, we provide necessary and sufficient conditions for several versions of Farkas lemmas to hold. Similarly, we provide characterizations for conic constrained optimization problems to have the strong or stable strong dualities such as Lagrange, Fenchel–Lagrange or Toland–Fenchel–Lagrange duality.  相似文献   

8.
The problems of (bi-)proportional rounding of a nonnegative vector or matrix, resp., are written as particular separable convex integer minimization problems. Allowing any convex (separable) objective function we use the notions of vector and matrix apportionment problems. As a broader class of problems we consider separable convex integer minimization under linear equality restrictions Ax = b with any totally unimodular coefficient matrix A. By the total unimodularity Fenchel duality applies, despite the integer restrictions of the variables. The biproportional algorithm of Balinski and Demange (Math Program 45:193–210, 1989) is generalized and derives from the dual optimization problem. Also, a primal augmentation algorithm is stated. Finally, for the smaller class of matrix apportionment problems we discuss the alternating scaling algorithm, which is a discrete variant of the well-known Iterative Proportional Fitting procedure.  相似文献   

9.
The main purpose of this paper is to study the duality and penalty method for a constrained nonconvex vector optimization problem. Following along with the image space analysis, a Lagrange-type duality for a constrained nonconvex vector optimization problem is proposed by virtue of the class of vector-valued regular weak separation functions in the image space. Simultaneously, some equivalent characterizations to the zero duality gap property are established including the Lagrange multiplier, the Lagrange saddle point and the regular separation. Moreover, an exact penalization is also obtained by means of a local image regularity condition and a class of particular regular weak separation functions in the image space.  相似文献   

10.
《Optimization》2012,61(4):541-560
This paper concerns a closedness condition called (CC) involving a convex function and a convex constrained system. This type of condition has played an important role in the study of convex optimization problems. Our aim is to establish several characterizations of this condition and to apply them to study problems of minimizing a DC function under a cone-convex constraint and a set constraint. First, we establish several so-called ‘Toland–Fenchel–Lagrange’ duality theorems. As consequences, various versions of generalized Farkas lemmas in dual forms for systems involving convex and DC functions are derived. Then, we establish optimality conditions for DC problem under convex constraints. Optimality conditions for convex problems and problems of maximizing a convex function under convex constraints are given as well. Most of the results are established under the (CC) condition. This article serves as a link between several corresponding known ones published recently for DC programs and for convex programs.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号