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121.
Multivalued convexity and optimization: A unified approach to inequality and equality constraints 总被引:5,自引:0,他引:5
J. Borwein 《Mathematical Programming》1977,13(1):183-199
Multivalued functions satisfying a general convexity condition are examined in the first section. The second section establishes a general transposition theorem for such functions and develops an abstract multiplier principle for them. In particular both convex inequality and linear equality constraints are seen to satisfy the same generalized constraint qualification. The final section examines quasi-convex programmes. 相似文献
122.
A kind of general convexification and concavification methods is proposed for solving some classes of global optimization problems with certain monotone properties. It is shown that these minimization problems can be transformed into equivalent concave minimization problem or reverse convex programming problem or canonical D.C. programming problem by using the proposed convexification and concavification schemes. The existing algorithms then can be used to find the global solutions of the transformed problems. 相似文献
123.
124.
Michael Nast 《Journal of Global Optimization》1996,9(1):65-93
In this article, our primary concern is the classical problem of minimizing globally a concave function over a compact polyhedron (Problem (P)). We present a new simplicial branch and bound approach, which combines triangulations of intersections of simplices with halfspaces and ideas from outer approximation in such a way, that a class of finite algorithms for solving (P) results. For arbitrary compact convex feasible sets one obtains a not necessarily finite but convergent algorithm. Theoretical investigations include determination of the number of simplices in each applied triangulation step and bounds on the number of iterations in the resulting algorithms. Preliminary numerical results are given, and additional applications are sketched. 相似文献
125.
A concave function defined on a polytope may have many local minima (in fact every extreme point may be a local minimum). Sufficient conditions are given such that if they are satisfied at a point, this point is known to be a global minimum. It is only required to solve a single linear program to test whether the sufficient conditions are satisfied. This test has been incorporated into an earlier algorithm to give improved performance. Computational results presented show that these sufficient conditions are satisfied for certain types of problems and may substantially reduce the effort needed to find and recognize a global minimum. 相似文献
126.
David Yang Gao 《Journal of Global Optimization》2006,35(1):131-143
This paper presents a set of complete solutions to a class of polynomial optimization problems. By using the so-called sequential canonical dual transformation developed in the author’s recent book [Gao, D.Y. (2000), Duality Principles in Nonconvex Systems: Theory, Method and Applications,
Kluwer Academic Publishers, Dordrecht/Boston/London, xviii + 454 pp], the nonconvex polynomials in
can be converted into an one-dimensional canonical dual optimization problem, which can be solved completely. Therefore,
a set of complete solutions to the original problem is obtained. Both global minimizer and local extrema of certain special
polynomials can be indentified by Gao-Strang’s gap function and triality theory. For general nonconvex polynomial minimization
problems, a sufficient condition is proposed to identify global minimizer. Applications are illustrated by several examples. 相似文献
127.
The problem of approximating m data points (x
i
, y
i
) in , with a quadratic function q(x, p) with s parameters, m ≥ s, is considered. The parameter vector is to be determined so as to satisfy three conditions: (1) q(x, p) must underestimate all m data points, i.e. q(x
i
, p) ≤ y
i
, i=1,...,m. (2) The error of the approximation is to be minimized in the L1 norm. (3) The eigenvalues of H are to satisfy specified lower and upper bounds, where H is the Hessian of q(x, p) with respect to x. This is called the Quadratic Underestimator with Bounds on Eigenvalues (QUBE) problem. An algorithm for its solution (QUBE algorithm) is given and justified, and computational results presented. The QUBE algorithm has application to finding the global minimum of a basin (or funnel) shaped function with a large number of local minima. Such problems arise in computational biology where it is desired to find the global minimum of an energy surface, in order to predict native protein-ligand docking geometry (drug design) or protein structure. Computational results for a simulated docking energy surface, with n=15, are presented. It is shown that specifying a small condition number for H improves the ability of the underestimator to correctly predict the global minimum point. 相似文献
128.
Effendi Widjaja Hui Heng Chong Martin Tjahjono 《Journal of Raman spectroscopy : JRS》2010,41(2):181-186
In situ thermo‐Raman spectroscopy (TRS) measurements were performed in order to investigate solid‐phase transformation of the copper sulfate pentahydrate from room temperature up to 300 °C. Band‐target entropy minimization (BTEM), a blind‐source separation algorithm, was employed in order to identify and reconstruct the pure component spectra of the species involved in the dehydration process. In spite of low signal‐to‐noise ratio and elevated baseline spectral data, BTEM was successfully utilized to identify and reconstruct four pure component spectra of copper sulfate pentahydrate, trihydrate, monohydrate, and anhydrate, which were formed during this thermally induced process. Subsequent mapping of these four pure component spectral estimates back onto the preprocessed spectra yielded the relative concentrations of each individual species. Finally, the transition temperatures of each dehydration step could be unambiguously deduced from the obtained concentration profile. The current study shows that combined thermo‐Raman spectroscopy and chemometric analysis provides an effective tool to determine the dehydration temperatures as well as to identify the structures of each individual species involved in a solid‐phase dehydration process. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
129.
第一原理电子结构计算已成为探索与研究物质机理、理解与预测材料性质的重要手段和工具.虽然第一原理电子结构计算取得了巨大的成功,但是如何利用高性能计算机又快又好地计算大规模体系,如何从数学角度理解电子结构模型的合理性与计算的可靠性和有效性,依然充满各种挑战.基于密度泛函理论的第一原理电子结构计算的核心数学模型为Kohn-Sham方程或相应的Kohn-Sham能量泛函极小问题.近年来,人们分别从非线性算子特征值问题的高效离散及Kohn-Sham能量泛函极小问题的最优化方法设计两个方面对电子结构计算的高效算法设计及分析展开了诸多研究.本文重点介绍我们小组在电子结构计算的方法与理论方面的一些进展,同时简单介绍该领域存在的困难与挑战. 相似文献
130.
Margarida Baía Farid Bozorgnia Léonard Monsaingeon Juha Videman 《Journal of Mathematical Analysis and Applications》2018,457(1):77-103
The objective of this work is to study a coupled system of degenerate and nonlinear partial differential equations governing the transport of reactive solutes in groundwater. We show that this system admits a unique weak solution provided the nonlinear adsorption isotherm associated with the reaction process satisfies certain physically reasonable structural conditions, by addressing a more general problem. In addition, we conclude, that the solute concentrations stay non-negative if the source term is componentwise non-negative and investigate numerically the finite speed of propagation of compactly supported initial concentrations, in a two-component test case. 相似文献