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Continuous Selections of the Set-Valued Metric Generalized Inverse in 2-Strictly Convex Banach Spaces
In this paper, we prove that if X is an almost convex and 2-strictly convex space, linear operator T : X → Y is bounded, N ( T ) is an approximative...
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Strictly Invariant Sets for 2-D Tent Maps: 2-D Strange Attractors
We study the existence of maximal strictly invariant compact sets for a certain two-parameter family of Expanding Baker Maps (EBMs), called 2-D tent...
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Mean Convex Smoothing of Mean Convex Cones
We show that any minimizing hypercone can be perturbed into one side to a properly embedded smooth minimizing hypersurface in the Euclidean space,...
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Convex Optimization
Convex optimization or convex programming refers to the problem of minimizing convex functions over convex sets. Observe that we have been careful to...
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Convex Functions
This chapter is devoted to convex functions, the rock star of optimization theory. In this section, we recall their key properties that matter for...
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Convex Non-convex Variational Models
An important class of computational techniques to solve inverse problems in image processing relies on a variational approach: the optimal output is...
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The First Width of Non-negatively Curved Surfaces with Convex Boundary
In this paper, free boundary geodesic networks whose length realizes the first min–max width of the length functional are investigated. This...
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Convex Sets
Recall that a convex set \(C \subset \mathcal {R}^d\) is a...
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Decomposition of an integrally convex set into a Minkowski sum of bounded and conic integrally convex sets
Every polyhedron can be decomposed into a Minkowski sum (or vector sum) of a bounded polyhedron and a polyhedral cone. This paper establishes similar...
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Morse–Smale complexes on convex polyhedra
Motivated by applications in geomorphology, the aim of this paper is to extend Morse–Smale theory from smooth functions to the radial distance...
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Convex Separation and Some Consequences
This chapter mainly concerns convex separation theorems that play a fundamental role in convex analysis and its numerous applications. We also study...
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Strongly convex matrix functions
In this article, we study strongly convex matrix functions and the strong Davis-Sherman condition to see their relations, corresponding to those of...
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Introduction to Convex Analysis
Convexity plays a major role in Optimization both in theory and in computational applications. Actually, convexity properties of optimization...
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Locally Convex Spaces
Recall that Theorems 2.6.4 and 2.6.7 established the HB...
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Fiber Convex Bodies
In this paper we study the fiber bodies, that is the extension of the notion of fiber polytopes for more general convex bodies. After giving an...
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Non-Convex Optimization of Resource Allocation in Fog Computing Using Successive Approximation
Fog computing can deliver low delay and advanced IT services to end users with substantially reduced energy consumption. Nevertheless, with soaring...