Results 201 to 210 of about 330,664 (214)

Convex programming for disjunctive convex optimization

Mathematical Programming, 1999
Given a finite number of closed convex sets whose algebraic representation is known, we study the problem of finding the minimum of a convex function on the closure of the convex hull of the union of those sets. We derive an algebraic characterization of the feasible region in a higher-dimensional space and propose a solution procedure akin to the ...
João Soares, Sebastián Ceria
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Duality in Convex Optimization

2011
A convex optimization problem can be paired with a dual problem involving the conjugates of the functions appearing in its (primal) formulation. In this chapter, we study the interplay between primal and dual problems in the context of Fenchel–Rockafellar duality and, more generally, for bivariate functions.
Heinz H. Bauschke, Patrick L. Combettes
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Smooth Convex Optimization

2004
In this chapter, we study the complexity of solving optimization problems formed by differentiable convex components. We start by establishing the main properties of such functions and deriving the lower complexity bounds, which are valid for all natural optimization methods.
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Convexity, Optimization, and Inequalities

2010
Convexity is one of the key concepts of mathematical analysis and has interesting consequences for optimization theory, statistical estimation, inequalities, and applied probability. Despite this fact, students seldom see convexity presented in a coherent fashion. It always seems to take a backseat to more pressing topics.
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A tutorial on convex optimization [PDF]

Proceedings of the 2004 American Control Conference, 2004
In recent years, convex optimization has become a computational tool of central importance in engineering, thanks to it's ability to solve very large, practical engineering problems reliably and efficiently. The goal of this tutorial is to give an overview of the basic concepts of convex sets, functions and convex optimization problems, so that the ...
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Nonsmooth Convex Optimization

2004
(Equivalent definitions; Closed functions; Continuity of convex functions; Separation theorems; Subgradients; Computation rules; Optimality conditions.)
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Advances in Convex Optimization

2006 Chinese Control Conference, 2006
In this talk I will give an overview of general convex optimization, which can be thought of as an extension of linear programming, and some recently developed subfamilies such as second-order cone, semidefinite, and geometric programming. Like linear programming, we have a fairly complete duality theory, and very effective numerical methods for these ...
Stephen Boyd, Michael C. Grant, Lieven Vandenberghe   +2 more
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Multimodularity, Convexity and Optimization

2003
1.1 Introduction 1.1.1 Organization of the chapter 1.2 Properties of multimodular functions 1.2.1 General properties 1.2.2 Multimodularity and convexity 1.3 The optimality of bracket policies for a single criterion 1.3.1 Upper Bounds 1.3.2 Lower Bounds 1.3.3 Optimality of the Bracket Sequences
Eitan Altman, Arie Hordijk, Bruno Gaujal
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Generalized Convexity and Optimization

2009
The authors have written a rigorous yet elementary and self-contained book to present, in a unified framework, generalized convex functions, which are the many non-convex functions that share at least one of the valuable properties of convex functions and which are often more suitable for describing real-world problems.
CAMBINI A, MARTEIN, LAURA
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Convex optimization theory

Optimization Methods and Software, 2010
Convex optimization theory, by Dimitri P. Bertsekas, Athena Scientific, June 2009, 256 pp., $59.00 (hardcover), ISBN: 1-886529-31-0, 978-1-886529-31-1 The textbook, Convex Optimization Theory (Athe...
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