共查询到20条相似文献,搜索用时 578 毫秒
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一个数学规划问题称为是自身对偶的,如果它可以从它的对偶问题中增加或减去某些约束条件而得到,而且它和它的对偶问题有相同的最优解和相同的最优值.凡是自身对偶的数学规划问题都有这样一些重要性质:它的最优值等于零,它的最优解在约束集合的边界上,等等。因此,自身对偶是一类非常重要的对偶模型,它在数学规划的对偶理论中,占有极其重要的地位。文章[1,2]分别讨论了自身对偶的线性规划问题和二次规划问题。文章[3]推广了文章[1]和[2]的结果,建立了如下一类自身对偶的凸规划问题 相似文献
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周志昂 《数学的实践与认识》2007,37(15):131-135
我们讨论了广义次似凸集值优化的对偶定理.首先,我们给出了广义次似凸集值优化的对偶问题.其次,我们给出了广义次似凸集值优化的对偶定理.最后,我们考虑了广义次似凸集值优化问题的标量化对偶,并给出了一系列对偶定理. 相似文献
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针对基于对偶犹豫模糊偏好信息的双边稳定匹配问题,提出了一种新的匹配方法.首先,给出了基于对偶犹豫模糊偏好信息的双边稳定匹配问题的描述;然后,依据双边主体给出的偏好信息构造对偶犹豫模糊偏好矩阵,使用投影技术将对偶犹豫模糊偏好矩阵转化为满意度矩阵;接着,以双方主体满意度最大化为目标,考虑稳定匹配的约束条件,构建了匹配模型;进而,运用组合满意度分析方法,将多目标优化模型转化为单目标优化模型,通过模型求解得到最优的匹配方案;最后,实例分析说明了所提方法的实用性和有效性. 相似文献
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We present in this paper new sufficient conditions for verifying zero duality gap in nonconvex quadratically/linearly constrained
quadratic programs (QP). Based on saddle point condition and conic duality theorem, we first derive a sufficient condition
for the zero duality gap between a quadratically constrained QP and its Lagrangian dual or SDP relaxation. We then use a distance
measure to characterize the duality gap for nonconvex QP with linear constraints. We show that this distance can be computed
via cell enumeration technique in discrete geometry. Finally, we revisit two sufficient optimality conditions in the literature
for two classes of nonconvex QPs and show that these conditions actually imply zero duality gap. 相似文献
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Phan Thien Thach 《Journal of Global Optimization》1993,3(3):311-324
The aim of this paper is to present a nonconvex duality with a zero gap and its connection with convex duality. Since a convex program can be regarded as a particular case of convex maximization over a convex set, a nonconvex duality can be regarded as a generalization of convex duality. The generalized duality can be obtained on the basis of convex duality and minimax theorems. The duality with a zero gap can be extended to a more general nonconvex problems such as a quasiconvex maximization over a general nonconvex set or a general minimization over the complement of a convex set. Several applications are given.On leave from the Institute of Mathematics, Hanoi, Vietnam. 相似文献
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This paper presents a canonical duality theory for solving a general nonconvex quadratic minimization problem with nonconvex
constraints. By using the canonical dual transformation developed by the first author, the nonconvex primal problem can be converted into a canonical dual problem with zero duality
gap. A general analytical solution form is obtained. Both global and local extrema of the nonconvex problem can be identified
by the triality theory associated with the canonical duality theory. Illustrative applications to quadratic minimization with
multiple quadratic constraints, box/integer constraints, and general nonconvex polynomial constraints are discussed, along
with insightful connections to classical Lagrangian duality. Criteria for the existence and uniqueness of optimal solutions
are presented. Several numerical examples are provided. 相似文献
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Lagrangian relaxation is often an efficient tool to solve (large-scale) optimization problems, even nonconvex. However it
introduces a duality gap, which should be small for the method to be really efficient. Here we make a geometric study of the
duality gap. Given a nonconvex problem, we formulate in a first part a convex problem having the same dual. This formulation
involves a convexification in the product of the three spaces containing respectively the variables, the objective and the
constraints. We apply our results to several relaxation schemes, especially one called “Lagrangean decomposition” in the combinatorial-optimization
community, or “operator splitting” elsewhere. We also study a specific application, highly nonlinear: the unit-commitment
problem.
Received: June 1997 / Accepted: December 2000?Published online April 12, 2001 相似文献
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Linh T. H. Nguyen 《Optimization》2018,67(2):195-216
Motivated by weakly convex optimization and quadratic optimization problems, we first show that there is no duality gap between a difference of convex (DC) program over DC constraints and its associated dual problem. We then provide certificates of global optimality for a class of nonconvex optimization problems. As an application, we derive characterizations of robust solutions for uncertain general nonconvex quadratic optimization problems over nonconvex quadratic constraints. 相似文献
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Giuseppe Buttazzo Faustino Maestre Bozhidar Velichkov 《Journal of Optimization Theory and Applications》2018,177(3):743-769
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
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《European Journal of Operational Research》2020,280(2):441-452
In this paper we show that a convexifiability property of nonconvex quadratic programs with nonnegative variables and quadratic constraints guarantees zero duality gap between the quadratic programs and their semi-Lagrangian duals. More importantly, we establish that this convexifiability is hidden in classes of nonnegative homogeneous quadratic programs and discrete quadratic programs, such as mixed integer quadratic programs, revealing zero duality gaps. As an application, we prove that robust counterparts of uncertain mixed integer quadratic programs with objective data uncertainty enjoy zero duality gaps under suitable conditions. Various sufficient conditions for convexifiability are also given. 相似文献
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Solutions and optimality criteria for nonconvex quadratic-exponential minimization problem 总被引:1,自引:0,他引:1
This paper presents a set of complete solutions and optimality conditions for a nonconvex quadratic-exponential optimization
problem. By using the canonical duality theory developed by the first author, the nonconvex primal problem in n-dimensional space can be converted into an one-dimensional
canonical dual problem with zero duality gap, which can be solved easily to obtain all dual solutions. Each dual solution
leads to a primal solution. Both global and local extremality conditions of these primal solutions can be identified by the
triality theory associated with the canonical duality theory. Several examples are illustrated. 相似文献
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R. Horst 《European Journal of Operational Research》1980,5(3):205-209
First a priori estimates of the duality gap in nonconvex programming are given by very easy arguments on well-known results in duality theory. Then a very simple procedure for solving bid evaluation type problems is deduced. 相似文献
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Mirjam Dür 《Journal of Global Optimization》2002,22(1-4):49-57
We investigate the problem of minimizing a nonconvex function with respect to convex constraints, and we study different techniques to compute a lower bound on the optimal value: The method of using convex envelope functions on one hand, and the method of exploiting nonconvex duality on the other hand. We investigate which technique gives the better bound and develop conditions under which the dual bound is strictly better than the convex envelope bound. As a byproduct, we derive some interesting results on nonconvex duality. 相似文献