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41.
Global Optimality Conditions in Maximizing a Convex Quadratic Function under Convex Quadratic Constraints 总被引:2,自引:0,他引:2
Jean-Baptiste Hiriart-Urruty 《Journal of Global Optimization》2001,21(4):443-453
For the problem of maximizing a convex quadratic function under convex quadratic constraints, we derive conditions characterizing a globally optimal solution. The method consists in exploiting the global optimality conditions, expressed in terms of -subdifferentials of convex functions and -normal directions, to convex sets. By specializing the problem of maximizing a convex function over a convex set, we find explicit conditions for optimality. 相似文献
42.
《Optimization》2012,61(2):133-161
The aim of this article is to give a survey of some basic theory of semi-infinite programming. In particular, we discuss various approaches to derivations of duality, discretization, and first- and second-order optimality conditions. Some of the surveyed results are well known while others seem to be less noticed in that area of research. 相似文献
43.
Using a general approach which provides sequential optimality conditions for a general convex optimization problem, we derive necessary and sufficient optimality conditions for composed convex optimization problems. Further, we give sequential characterizations for a subgradient of the precomposition of a K-increasing lower semicontinuous convex function with a K-convex and K-epi-closed (continuous) function, where K is a nonempty convex cone. We prove that several results from the literature dealing with sequential characterizations of subgradients are obtained as particular cases of our results. We also improve the above mentioned statements. 相似文献
44.
Achiya Dax 《Mathematical Programming》1986,36(1):72-80
Thekey problem of the Euclidean multifacility location (EMFL) problem is to decide whether a givendead point is optimal. If it is not optimal, we wish to compute a descent direction. This paper extends the optimality conditions of
Calamai and Conn and Overton to the case when the rows of the active constraints matrix are linearly dependent. We show that
linear dependence occurs wheneverG, the graph of the coinciding facilities, has a cycle. In this case the key problem is formulated as a linear least squares
problem with bounds on the Euclidean norms of certain subvectors. 相似文献
45.
Christian Lubich. 《Mathematics of Computation》2005,74(250):765-779
The Dirac-Frenkel-McLachlan variational principle is the basic tool for obtaining computationally accessible approximations in quantum molecular dynamics. It determines equations of motion for an approximate time-dependent wave function on an approximation manifold of reduced dimension. This paper gives a near-optimality result for variational approximations. It bounds the error in terms of the distance of the exact wave function to the approximation manifold and identifies the parameters that control the deviation of the variational approximation from the best approximation on the manifold.
46.
V. P. Godambe 《Annals of the Institute of Statistical Mathematics》1999,51(2):201-215
In non-Bayesian statistics, it is often realistic to replace a full distributional assumption by a much weaker assumption about its first few moments; such as for instance, mean and variance. Along the same lines in Bayesian statistics one may wish to replace a completely specified prior distribution by an assumption about just a few moments of the distribution. To deal with such Bayesian semi-parametric models defined only by a few moments, Hartigan (1969, J. Roy. Statist. Soc. Ser. B, 31, 440-454) put forward linear Bayes methodology. By now it has become a standard tool in Bayesian analysis. In this paper we formulate an alternative methodology based on the theory of optimum estimating functions. This alternative methodology is shown to be more readily applicable and efficient in common problems, than the linear Bayes methodology mentioned above. 相似文献
47.
The Maximum Clique Problem (MCP) is regarded here as the maximization of an indefinite quadratic form over the canonical simplex. For solving MCP an algorithm based upon Global Optimality Conditions (GOC) is applied. Furthermore, each step of the algorithm is analytically investigated and tested. The computational results for the proposed algorithm are compared with other Global Search approaches. 相似文献
48.
非凸半定规划的广义Fakars引理及最优性条件 总被引:1,自引:0,他引:1
1引言在本文中,我们用(?),S~n,S_ ~n分别表示有限维向量空间,n阶对称矩阵空间及n阶半正定矩阵锥.我们考虑如下形式的非凸半定规划问题: 相似文献
49.
A fast Pareto genetic algorithm approach for solving expensive multiobjective optimization problems 总被引:1,自引:0,他引:1
We present a new multiobjective evolutionary algorithm (MOEA), called fast Pareto genetic algorithm (FastPGA), for the simultaneous
optimization of multiple objectives where each solution evaluation is computationally- and/or financially-expensive. This
is often the case when there are time or resource constraints involved in finding a solution. FastPGA utilizes a new ranking
strategy that utilizes more information about Pareto dominance among solutions and niching relations. New genetic operators
are employed to enhance the proposed algorithm’s performance in terms of convergence behavior and computational effort as
rapid convergence is of utmost concern and highly desired when solving expensive multiobjective optimization problems (MOPs).
Computational results for a number of test problems indicate that FastPGA is a promising approach. FastPGA yields similar
performance to that of the improved nondominated sorting genetic algorithm (NSGA-II), a widely-accepted benchmark in the MOEA
research community. However, FastPGA outperforms NSGA-II when only a small number of solution evaluations are permitted, as
would be the case when solving expensive MOPs. 相似文献
50.