A general cone decomposition theory based on efficiency

Martínez-Legaz, Juan Enrique; Seeger, Alberto

doi:10.1007/bf01581687

Cited by 4 publications

(2 citation statements)

References 11 publications

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“…In [4] we obtained new results for finite-dimensional spaces and proved that there exist approximate solutions of the splitting problem for Lipschitz selections in the Hilbert space. We also wish to mention [13] and [15], where related questions were considered.…”

Section: Introductionmentioning

confidence: 99%

Uniform convexity and the splitting problem for selections

Balashov

Repovš

2009

Journal of Mathematical Analysis and Applications

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We continue to investigate cases when the Repov\v{s}-Semenov splitting problem for selections has an affirmative solution for continuous set-valued mappings. We consider the situation in infinite-dimensional uniformly convex Banach spaces. We use the notion of Polyak of uniform convexity and modulus of uniform convexity for arbitrary convex sets (not necessary balls). We study general geometric properties of uniformly convex sets. We also obtain an affirmative solution of the splitting problem for selections of certain set-valued mappings with uniformly convex images

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Section: Introductionmentioning

confidence: 99%

Uniform convexity and the splitting problem for selections

Balashov

Repovš

2009

Journal of Mathematical Analysis and Applications

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“…A cone decomposition theory based on efficiency has been developed by J.E. Martinez Legaz and A. Seeger in [4]. a cone K, this property is equivalent to the following: the space E with the order relation generated by K possesses the Riesz interpolation property.…”

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confidence: 99%

Conical Decomposition and Vector Lattices With Respect to Several Preorders

Baratov¹,

Rubinov²

2006

Taiwanese J. Math.

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The decomposition set-valued mapping in a Banach space E with cones K i , i = 1, . . . , n describes all decompositions of a given element on addends, such that addend i belongs to the i-th cone. We examine the decomposition mapping and its dual.We study conditions that provide the additivity of the decomposition mapping. For this purpose we introduce and study the Riesz interpolation property and lattice properties of spaces with respect to several preorders. The notion of 2-vector lattice is introduced and studied. Theorems that establish the relationship between the Riesz interpolation property and lattice properties of the dual spaces are given.

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Improving the efficiency of DC global optimization methods by improving the DC representation of the objective function

Ferrer

Martínez-Legaz

2008

J Glob Optim

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There are infinitely many ways of representing a d.c. function as a difference of convex functions. In this paper we analyze how the computational efficiency of a d.c. optimization algorithm depends on the representation we choose for the objective function, and we address the problem of characterizing and obtaining a computationally optimal representation. We introduce some theoretical concepts which are necessary for this analysis and report some numerical experiments.

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A general cone decomposition theory based on efficiency

Cited by 4 publications

References 11 publications

Uniform convexity and the splitting problem for selections

Uniform convexity and the splitting problem for selections

Conical Decomposition and Vector Lattices With Respect to Several Preorders

Improving the efficiency of DC global optimization methods by improving the DC representation of the objective function

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