Results 281 to 290 of about 615,016 (327)
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Fundamentals of Convex Analysis
2001International ...
Hiriart-Urruty, Jean-Baptiste +1 more
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Sbornik: Mathematics, 1996
Summary: 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.
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Summary: 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.
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Convexity in complex analysis [PDF]
Banach Center Publications, 1995 Convexity is the key concept of functional analysis, but apart from some notable exceptions, it has played a relatively minor role in several complex variables theory. The work of Lempert has focused attention on convex domains, and in these two lectures I will present examples involving invariant metrics in complex analysis where convexity, whether ...
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Abstract Convexity in Measure Theory and in Convex Analysis
Journal of Mathematical Sciences, 2003The paper under report is a survey on the so-called ``abstract convex analysis'' and on some applications to optimization problems. If \(\Omega\) is a set and \(H\) is a class of functions from \(\Omega\) into \(\mathbb{R}\), a function \(f: \Omega\to\mathbb{R}\cup \{+\infty\}\) is called \(H\)-convex if it is the supremum of a family of functions ...
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1993
In classical real analysis, the gradient of a differentiable function f : ℝn → ℝ. plays a key role - to say the least. Considering this gradient as a mapping x ↦ s(x) = ∇f(x) from (some subset X of) ℝn to (some subset S of) ℝn, an interesting object is then its inverse: to a given s ∈ S, associate the x ∈ X such that s = ∇f(x).
Claude Lemaréchal +1 more
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In classical real analysis, the gradient of a differentiable function f : ℝn → ℝ. plays a key role - to say the least. Considering this gradient as a mapping x ↦ s(x) = ∇f(x) from (some subset X of) ℝn to (some subset S of) ℝn, an interesting object is then its inverse: to a given s ∈ S, associate the x ∈ X such that s = ∇f(x).
Claude Lemaréchal +1 more
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A convex analysis approach for convex multiplicative programming
Journal of Global Optimization, 2007Global optimization problems involving the minimization of a product of convex functions on a convex set are addressed in this paper. Elements of convex analysis are used to obtain a suitable representation of the convex multiplicative problem in the outcome space, where its global solution is reduced to the solution of a sequence of quasiconcave ...
Rúbia M. Oliveira, Paulo Ferreira
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Convex Functionals on Convex Sets and Convex Analysis
1985Over the last 20 years, parallel to the theory of monotone operators, a calculus for the investigation of convex functionals designated by convex analysis has emerged, which allows one to solve a number of problems in a simple way. To this calculus belong: (α) The subgradient ∂F (a generalization of the classical concept of derivative).
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Solution of a problem of convex analysis
Russian Mathematical Surveys, 1987See the review in Zbl 0633.49009.
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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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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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