共查询到19条相似文献,搜索用时 59 毫秒
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讨论非线性半定规划的四个专题, 包括半正定矩阵锥的变分分析、非凸半定规划问题的最优性条件、非凸半定规划问题的扰动分析和非凸半定规划问题的增广Lagrange方法. 相似文献
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本文首先将半定规划转化为一个变分不等式问题,在满足单调性和Lipschitz连续的条件下,提出了一种基于Korpelevich-Khobotv算法的新的预测-校正算法,并给出算法的收敛性分析. 相似文献
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迄今为止,还未见出版过有关求解非凸半定规划的算法,但在最近,Chen,et.al(2000)和Sun&Sun(1999)关于非凸半定规划(SDP)的增广Lagrangian的研究是非常有用的,在本文中,我们证明非凸半定规划的增广Lagrangian是可微的,并且给出它的可微表达式. 相似文献
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解半定规划的二次摄动方法 总被引:3,自引:0,他引:3
半定规划在系统论,控制论,组合优化,和特征值优化等领域有着广泛的应用。本文将半定规划摄动成二次半定规划,它的唯一解恰为原问题的解,并且对其偶问题等价于一个线性对称的投影方程,可方便地用投影收缩方法求解,从而获得原半定规划问题的解。文章给出了算法及其收敛性分析,数值试验结果表明摄动方法是解半定规划的一种有效的方法。 相似文献
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基于变换X=VV~T,本文将半定规划问题转换为非线性规划问题,提出了解决此问题的增广拉格朗日算法,并证明了算法的线性收敛性.在此算法中,每一次迭代计算的子问题利用最速下降搜索方向和满足wolf条件的线性搜索法求最优解.数值实验表明,此算法是行之有效的,且优于内点算法. 相似文献
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本文提出了解非线性半定规划的信赖域型过滤集-逐次线性化方法,该方法基于Fletcher和Leyffer 2002年提出的解非线性规划的过滤集的概念.本文给出了新的算法,并在较弱的条件下证明了算法的总体收敛性.最后,我们报告了新方法的数值结果,表明新方法是有效的. 相似文献
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N. L. Boland 《Mathematical Programming》1996,78(1):1-27
Because of the many important applications of quadratic programming, fast and efficient methods for solving quadratic programming
problems are valued. Goldfarb and Idnani (1983) describe one such method. Well known to be efficient and numerically stable,
the Goldfarb and Idnani method suffers only from the restriction that in its original form it cannot be applied to problems
which are positive semi-definite rather than positive definite. In this paper, we present a generalization of the Goldfarb
and Idnani method to the positive semi-definite case and prove finite termination of the generalized algorithm. In our generalization,
we preserve the spirit of the Goldfarb and Idnani method, and extend their numerically stable implementation in a natural
way.
Supported in part by ATERB, NSERC and the ARC.
Much of this work was done in the Department of Mathematics at the University of Western Australia and in the Department of
Combinatorics and Optimization at the University of Waterloo. 相似文献
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《Optimization》2012,61(5):713-733
This article develops the deterministic approach to duality for semi-definite linear programming problems in the face of data uncertainty. We establish strong duality between the robust counterpart of an uncertain semi-definite linear programming model problem and the optimistic counterpart of its uncertain dual. We prove that strong duality between the deterministic counterparts holds under a characteristic cone condition. We also show that the characteristic cone condition is also necessary for the validity of strong duality for every linear objective function of the original model problem. In addition, we derive that a robust Slater condition alone ensures strong duality for uncertain semi-definite linear programs under spectral norm uncertainty and show, in this case, that the optimistic counterpart is also computationally tractable. 相似文献
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We will propose a new and practical method for estimating the failure probability of a large number of small to medium scale companies using their balance sheet data. We will use the maximum likelihood method to estimate the best parameters of the logit function, where the failure intensity function in its exponent is represented as a convex quadratic function instead of a commonly used linear function. The reasons for using this type of function are : (i) it can better represent the observed nonlinear dependence of failure probability on financial attributes, (ii) the resulting likelihood function can be maximized using a cutting plane algorithm developed for nonlinear semi-definite programming problems.We will show that we can achieve better prediction performance than the standard logit model, using thousands of sample companies.Revised: December 2002, 相似文献
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Y. Evtushenko 《Journal of Optimization Theory and Applications》1977,21(2):121-135
Our aim here is to present numerical methods for solving a general nonlinear programming problem. These methods are based on transformation of a given constrained minimization problem into an unconstrained maximin problem. This transformation is done by using a generalized Lagrange multiplier technique. Such an approach permits us to use Newton's and gradient methods for nonlinear programming. Convergence proofs are provided, and some numerical results are given. 相似文献
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We analyze the rate of local convergence of the augmented Lagrangian method in nonlinear semidefinite optimization. The presence
of the positive semidefinite cone constraint requires extensive tools such as the singular value decomposition of matrices,
an implicit function theorem for semismooth functions, and variational analysis on the projection operator in the symmetric
matrix space. Without requiring strict complementarity, we prove that, under the constraint nondegeneracy condition and the
strong second order sufficient condition, the rate of convergence is linear and the ratio constant is proportional to 1/c, where c is the penalty parameter that exceeds a threshold .
The research of Defeng Sun is partly supported by the Academic Research Fund from the National University of Singapore. The
research of Jie Sun and Liwei Zhang is partly supported by Singapore–MIT Alliance and by Grants RP314000-042/057-112 of the
National University of Singapore. The research of Liwei Zhang is also supported by the National Natural Science Foundation
of China under project grant no. 10471015 and by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,
State Education Ministry, China. 相似文献
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N. B. Waite 《Journal of Optimization Theory and Applications》1994,80(3):537-549
We establish a smooth positive extension theorem: Given any closed subset of a finite-dimensional real Euclidean space, a function zero on the closed set can be extended to a function smooth on the whole space and positive on the complement of the closed set. This result was stimulated by nonlinear programming. We give several applications of this result to nonlinear programming.This paper is dedicated to the memory of Emily Sue Merkle Waite, Ph.D.The author wishes to thank W. Cunningham for suggesting the question about constraint qualifications, A. Karr for noticing the example of a Brownian motion sample path, R. Byrd and P. Hartman for discussions, and E. Waite for support and encouragement. 相似文献
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On programming when the positive cone has an empty interior 总被引:1,自引:0,他引:1
In this note, we present a condition which is equivalent to the existence of the Lagrange multiplier for the general convex programming problem. This condition enables one to study a hypothesis distinct from the one of nonempty interior of the positive cone of the space of restrictions that is commonly used. Simple examples of this condition are given. We also explore the relationship of this condition with the subdifferentiability of the primal functional. 相似文献
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The Roppenecker [11] parameterization of multi-input eigenvalue assignment, which allows for common open- and closed-loop eigenvalues, provides a platform for the investigation of several issues of current interest in robust control. Based on this parameterization, a numerical optimization method for designing a constant gain feedback matrix which assigns the closed-loop eigenvalues to desired locations such that these eigenvalues have low sensitivity to variations in the open-loop state space model was presented in Owens and O'Reilly [8]. In the present paper, two closely related numerical optimization methods are presented. The methods utilize standard (NAG library) unconstrained optimization routines. The first is for designing a minimum gain state feedback matrix which assigns the closed-loop eigenvalues to desired locations, where the measure of gain taken is the Frobenius norm. The second is for designing a state feedback matrix which results in the closed-loop system state matrix having minimum condition number. These algorithms have been shown to give results which are comparable to other available algorithms of far greater conceptual complexity. 相似文献
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