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111.
In this paper, we study the Riemannian length of the primal central path in a convex set computed with respect to the local
metric defined by a self-concordant function. Despite some negative examples, in many important situations, the length of
this path is quite close to the length of a geodesic curve. We show that in the case of a bounded convex set endowed with
a ν-self-concordant barrier, the length of the central path is within a factor O(ν
1/4) of the length of the shortest geodesic curve.
This paper presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian
State, Prime Minister’s Office, Science Policy Programming. 相似文献
112.
The approximation of the convex envelope of nonconvex functions is an essential part in deterministic global optimization
techniques (Floudas in Deterministic Global Optimization: Theory, Methods and Application, 2000). Current convex underestimation
algorithms for multilinear terms, based on arithmetic intervals or recursive arithmetic intervals (Hamed in Calculation of
bounds on variables and underestimating convex functions for nonconvex functions, 1991; Maranas and Floudas in J Global Optim
7:143–182, (1995); Ryoo and Sahinidis in J Global Optim 19:403–424, (2001)), introduce a large number of linear cuts. Meyer
and Floudas (Trilinear monomials with positive or negative domains: Facets of convex and concave envelopes, pp. 327–352, (2003);
J Global Optim 29:125–155, (2004)), introduced the complete set of explicit facets for the convex and concave envelopes of
trilinear monomials with general bounds. This study proposes a novel method to underestimate posynomial functions of strictly
positive variables. 相似文献
113.
We prove convex ordering results for random vectors admitting a predictable representation in terms of a Brownian motion and
a non-necessarily independent jump component. Our method uses forward-backward stochastic calculus and extends the results
proved in Klein et al. (Electron J Probab 11(20):27, 2006) in the one-dimensional case. We also study a geometric interpretation of convex ordering for discrete measures in connection
with the conditions set on the jump heights and intensities of the considered processes.
The work described in this paper was partially supported by a grant from City University of Hong Kong (Project No. 7200108). 相似文献
114.
In the literature, methods for the construction of piecewise linear upper and lower bounds for the approximation of univariate convex functions have been proposed. We study the effect of the use of transformations on the approximation of univariate (convex) functions. In this paper, we show that these transformations can be used to construct upper and lower bounds for nonconvex functions. Moreover, we show that by using such transformations of the input variable or the output variable, we obtain tighter upper and lower bounds for the approximation of convex functions than without these approximations. We show that these transformations can be applied to the approximation of a (convex) Pareto curve that is associated with a (convex) bi-objective optimization problem. 相似文献
115.
Our problem of interest consists of minimizing a separable, convex and differentiable function over a convex set, defined by bounds on the variables and an explicit constraint described by a separable convex function. Applications are abundant, and vary from equilibrium problems in the engineering and economic sciences, through resource allocation and balancing problems in manufacturing, statistics, military operations research and production and financial economics, to subproblems in algorithms for a variety of more complex optimization models. This paper surveys the history and applications of the problem, as well as algorithmic approaches to its solution. The most common techniques are based on finding the optimal value of the Lagrange multiplier for the explicit constraint, most often through the use of a type of line search procedure. We analyze the most relevant references, especially regarding their originality and numerical findings, summarizing with remarks on possible extensions and future research. 相似文献
116.
Maarten H. van der Vlerk 《Mathematical Methods of Operations Research》2005,62(2):225-242
We consider multiple simple recourse (MSR) models, both continuous and integer versions, which generalize the corresponding
simple recourse (SR) models by allowing for a refined penalty cost structure for individual shortages and surpluses. It will
be shown that (convex approximations of) such MSR models can be represented as explicitly specified continuous SR models,
and thus can be solved efficiently by existing algorithms.
This research has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. 相似文献
117.
The concepts of differentiability, convexity, generalized convexity and minimization of a fuzzy mapping are known in the literature. The purpose of this present paper is to extend and generalize these concepts to fuzzy mappings of several variables using Buckley–Feuring approach for fuzzy differentiation and derive Karush–Kuhn–Tucker condition for the constrained fuzzy minimization problem. 相似文献
118.
We present algorithms for decomposing a polygon (with holes) into convex polygons by diagonals. The methods are computationally
quick, and although the partitions that they produce may not have minimal cardinality they usually have a low number of convex
pieces. Thus, the methods are suitable for being used when achieving a modest load on the CPU time is more important than
finding optimal decompositions as, for instance, in location problems.
Part of the results in this paper are from Fernández (1999), and were presented in Fernández et al. (1998). This work has been supported by the Ministry of Science and Technology of Spain under the research projects BEC2002-01026,
SEJ2005-06273/ECON (J. Fernández, B. Tóth and B. Pelegrín) and TIC2003-05982-C05-03 (L. Cánovas), in part financed by the
European Regional Development Fund (ERDF). 相似文献
119.
Kazutoshi Ando 《Discrete Mathematics》2006,306(24):3181-3188
A pair (X,τ) of a finite set X and a closure operator τ:2X→2X is called a closure space. The class of closure spaces includes matroids as well as antimatroids. Associated with a closure space (X,τ), the extreme point operator ex:2X→2X is defined as ex(A)={p|p∈A,p∉τ(A-{p})}. We give characterizations of extreme point operators of closure spaces, matroids and antimatroids, respectively. 相似文献
120.
Gaëlle Semard Valerie Peulon-Agasse Auguste Bruchet Jean-Philippe Bouillon Pascal Cardinaël 《Journal of chromatography. A》2010,1217(33):5449-5454
It is important to develop methods of optimizing the selection of column sets and operating conditions for comprehensive two-dimensional gas chromatography. A new method for the calculation of the percentage of separation space used was developed using Delaunay's triangulation algorithms (convex hull). This approach was compared with an existing method and showed better precision and accuracy. It was successfully applied to the selection of the most convenient column set and the geometrical parameters of second column for the analysis of 49 target compounds in wastewater. 相似文献