Results 291 to 300 of about 314,907 (301)

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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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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Nonsmooth Convex Optimization

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

2020
In this chapter, we focus on stochastic convex optimization problems which have found wide applications in machine learning. We will first study two classic methods, i.e., stochastic mirror descent and accelerated stochastic gradient descent methods.
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Convex Grey Optimization

RAIRO - Operations Research, 2019
Many optimization problems are formulated from a real scenario involving incomplete information due to uncertainty in reality. The uncertainties can be expressed with appropriate probability distributions or fuzzy numbers with a membership function, if enough information can be accessed for the construction of either the probability density function or
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Deterministic Convex Optimization

2020
In this chapter, we study algorithms for solving convex optimization problems. We will focus on algorithms that have been applied or have the potential to be applied for solving machine learning and other data analysis problems. More specifically, we will discuss first-order methods which have been proven effective for large-scale optimization.
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A Convex Optimization Toolbox

2019
This chapter presents the duality theory for optimization problems, by both the minimax and perturbation approach, in a Banach space setting. Under some stability (qualification) hypotheses, it is shown that the dual problem has a nonempty and bounded set of solutions.
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