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Preliminaries: Convex Analysis and Convex Programming
2001In this chapter, we give some definitions and results connected with convex analysis, convex programming, and Lagrangian duality. In Part Two, these concepts and results are utilized in developing suitable optimality conditions and numerical methods for solving some convex problems.
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Computer Graphics and Image Processing, 1972
The analysis of shape is not well understood. To further our understanding it seemsreasonable to concentrate on one aspect of the problem. This paper deals with the analysis of convex blobs. The aim of the analysis is to extract fragments of a blob which are perceptually meaningful. This is done by attributing to each point a set of neigh boring points
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The analysis of shape is not well understood. To further our understanding it seemsreasonable to concentrate on one aspect of the problem. This paper deals with the analysis of convex blobs. The aim of the analysis is to extract fragments of a blob which are perceptually meaningful. This is done by attributing to each point a set of neigh boring points
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Sbornik: Mathematics, 1996
Properties of strongly convex sets (that is, of sets that can be represented as intersections of balls of radius fixed for each particular set) are investigated. A connection between strongly convex sets and strongly convex functions is established. The concept of a strongly convex R-hull of a set (the minimal strongly convex set containing the given ...
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Properties of strongly convex sets (that is, of sets that can be represented as intersections of balls of radius fixed for each particular set) are investigated. A connection between strongly convex sets and strongly convex functions is established. The concept of a strongly convex R-hull of a set (the minimal strongly convex set containing the given ...
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Elements of Convex Analysis [PDF]
, 1985 The purpose of this chapter is to provide some notions and fundamental results of convex analysis which will be used throughout this book. Starting with the notion of convexity, some propositions on convex and lower semi-continuous functionals as well as on the minimization of functionals on convex sets are given.
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Springer Series in Operations Research and Financial Engineering, 2022
B. Mordukhovich, Nguyen Mau Nam
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B. Mordukhovich, Nguyen Mau Nam
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Stabilization Problems with Constraints, 2021
V. Bushenkov, G. Smirnov
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V. Bushenkov, G. Smirnov
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2000
In this chapter a theory of discrete optimization called discrete convex analysis will be introduced. For a comprehensive treatment we refer the reader to Stoer and Witzgall [227], Fujishige [96, Chapter IV], and Murota [179] [181]. Martinez-Legaz [165] seems to have been the first writer to apply the discrete convex analysis to the cooperative game ...
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In this chapter a theory of discrete optimization called discrete convex analysis will be introduced. For a comprehensive treatment we refer the reader to Stoer and Witzgall [227], Fujishige [96, Chapter IV], and Murota [179] [181]. Martinez-Legaz [165] seems to have been the first writer to apply the discrete convex analysis to the cooperative game ...
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Convex analysis and minimization algorithms
, 1993J. Hiriart-Urruty, C. Lemaréchal
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Convexity and Variational Analysis
2013The paper focuses on the interplay between methods of general variational analysis, on the one hand, and convex analysis, on the other (with a special emphasis on the efficiency of the latter), in treating problems that come from the general variational analysis when applied in substantial or virtual presence of convexity.
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