7 edition of **Discrete Convex Analysis (Monographs on Discrete Math and Applications) (Monographs on Discrete Mathematics and Applications)** found in the catalog.

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Discrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete Cited by: Discrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete optimization.

The study of this theory is expanding with the development of efficient algorithms and applications to a number of. Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other areas.

The book gives an overview of major results, methods and ideas of convex and discrete geometry and its applications. Besides being a graduate-level introduction to the field, it is a practical source of information and orientation for convex by: Discrete Convex Analysis is a Discrete Convex Analysis book paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular.

Discrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete optimization.2/5(1).

Discrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete optimization.

Fundamental properties of L-convex functions are established in this chapter, including the local optimality criterion for global optimality the proximity theorem for minimizers, discrete midpoint convexity, integral convexity, and extensibility to convex functions.

Duality and conjugacy issues are treated in Chapter 8 and algorithms in Chapter Mathematical Programming No. P, Revised Version Abstract A theory of “discrete convex analysis” is developed for integer-valued functions deﬁned on integer lattice points.

Discrete convexity, in particular, L ♮ ‐convexity and M ♮ ‐convexity, provides a critical opening to attack several classical problems in inventory theory, as well as many other operations problems that arise from more recent practices, for instance, appointment scheduling and bike sharing.

As a powerful framework, discrete convex analysis is becoming increasingly popular in the Author: Xin Chen, Menglong Li. ABSTRACT This paper presents discrete convex analysis as a tool for use in economics and game theory. Discrete convex analysis is a new framework of discrete mat- hematics and optimization, developed during the last two decades.

Recently, it has been recognized as a powerful tool for analyzing economic or game models with indivisibilities. Abstract A theory of “discrete convex analysis” is developed for integer-valued functions defined on integer lattice points.

A theory of “discrete convex analysis” is developed for integer-valued functions defined on integer lattice points. The theory parallels the ordinary convex analysis, covering discrete analogues of the fundamental concepts such as conjugacy, subgradients, the Fenchel min-max duality, separation theorems and the Lagrange duality framework for convex/nonconvex optimization.

Based on the book “Convex Optimization Theory,” Athena Scientiﬁc,including the on-line Chapter 6 and supple- •Continuous vs discrete problem distinction ⌅ • Convex programming problems are those for which.

and. •The machinery of convex analysis is needed to ﬂesh out this ﬁgure, and to rule out the excep. In discrete convex analysis, the scaling and proximity properties for the class of L$^\natural$-convex functions were established more than a decade ago and have been used to design efficient.

Discrete convex analysis [18, 40, 43, 47] aims to establish a general theoretical framework for solv-able discrete optimization problems by means of a combination of the ideas in continuous optimiza-tion and combinatorial optimization.

The framework of convex analysis is adapted to discrete set. Keywords: Convex programs, discrete version of topics in analysis, time scales calcu-lus. 1 Introduction Convex optimization, a branch of mathematical optimization theory, has been developed in two directions. The real convex optimization and the discrete (or combinatorial) con-vex optimization.

when mathematical operations on convex functions are involved, and the calculus of conjugate functions can be brought to bear for analysis or com-putation.

The book evolved from the earlier book of the author [BNO03] on the subject (coauthored with A. Nedi´c and. Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other areas.

The book gives an overview of major. Network Optimization: Continuous and Discrete Models, Athena Scientific, ; click here for a copy of the book. Convex Optimization Theory, Athena Scientific, ; click here for a copy of the book. Convex Optimization Algorithms, Athena Scientific, Nonlinear Programming, 3rd edition Athena Scientific, Based on the book “Convex Optimization Theory,” Athena Scientiﬁc, •Continuous vs discrete problem distinction ⌅ • Convex programming problems are those for which.

and. •The machinery of convex analysis is needed to ﬂesh out this ﬁgure, and to rule out the excep. Publisher Summary. Convex sets and convex functions are studied in this chapter in the setting of n-dimensional Euclidean space R ity is an attractive subject to study, for many reasons; it draws upon geometry, analysis, linear algebra, and topology, and it has a role to play in such topics as classical optimal control theory, game theory, linear programming, and convex programming.Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other areas.

The book gives an overview of major results, methods and ideas of convex and discrete geometry and its applications."Discrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete optimization.