By Stephen Boyd, Lieven Vandenberghe

ISBN-10: 0521833787

ISBN-13: 9780521833783

Convex optimization difficulties come up usually in lots of various fields. A complete advent to the topic, this booklet exhibits intimately how such difficulties will be solved numerically with nice potency. the point of interest is on spotting convex optimization difficulties after which discovering the main acceptable approach for fixing them. The textual content comprises many labored examples and homework routines and may entice scholars, researchers and practitioners in fields resembling engineering, computing device technological know-how, arithmetic, facts, finance, and economics.

Show description

Read or Download Convex Optimization PDF

Best linear programming books

R. Tyrrell Rockafellar, Roger J.-B. Wets, Maria Wets's Variational analysis PDF

From its origins within the minimization of indispensable functionals, the thought of 'variations' has advanced drastically in reference to functions in optimization, equilibrium, and keep an eye on. It refers not just to limited circulation clear of some degree, but additionally to modes of perturbation and approximation which are top describable by way of 'set convergence', variational convergence of services' and so forth.

New PDF release: The SIAM 100-Digit Challenge: A Study in High-Accuracy

It is a stable booklet containing much approximately excessive accuracy computation. Ten difficulties are mentioned with information concerning many parts of arithmetic. loads of codes of many arithmetic software program are proven with a important appendix. an online web page of this e-book can also be a spotlight. you may also perform with it exhaustingly and enjoyably.

B. Luderer, L. Minchenko, T. Satsura's Multivalued Analysis and Nonlinear Programming Problems with PDF

From the reviews:"The target of this e-book is to check limitless dimensional areas, multivalued mappings and the linked marginal services … . the fabric is gifted in a transparent, rigorous demeanour. along with the bibliographical reviews … references to the literature are given in the textual content. … the unified method of the directional differentiability of multifunctions and their linked marginal features is a amazing function of the ebook … .

Download e-book for iPad: Hierarchical Optimization and Mathematical Physics by Vladimir Tsurkov

This e-book can be regarded as an advent to a unique dass of hierarchical platforms of optimum regulate, the place subsystems are defined by way of partial differential equations of varied kinds. Optimization is performed by way of a two-level scheme, the place the guts optimizes coordination for the higher point and subsystems locate the optimum options for self sufficient neighborhood difficulties.

Extra resources for Convex Optimization

Sample text

En ∈ Rn . It is the set of vectors that satisfy x 0, 1T x = 1. Vectors in the probability simplex correspond to probability distributions on a set with n elements, with xi interpreted as the probability of the ith element. 6), we proceed as follows. By definition, x ∈ C if and only if x = θ0 v0 + θ1 v1 + · · · + θk vk for some θ 0 with 1T θ = 1. Equivalently, if we define y = (θ1 , . . 8) for some y 0 with 1T y ≤ 1. Now we note that affine independence of the points v0 , . . , vk implies that the matrix B has rank k.

17) These inequalities are infeasible if and only if the (convex) sets C = {b − Ax | x ∈ Rn }, m D = Rm | y ≻ 0} ++ = {y ∈ R do not intersect. The set D is open; C is an affine set. , a nonzero λ ∈ Rm and µ ∈ R such that λT y ≤ µ on C and λT y ≥ µ on D. Each of these conditions can be simplified. The first means λT (b − Ax) ≤ µ for all x. 19) that AT λ = 0 and λT b ≤ µ. The second inequality means λT y ≥ µ for all y ≻ 0. This implies µ ≤ 0 and λ 0, λ = 0. 17) is infeasible if and only if there exists λ ∈ Rm such that λ = 0, λ 0, AT λ = 0, λT b ≤ 0.

1 Generalized inequalities 43 Generalized inequalities Proper cones and generalized inequalities A cone K ⊆ Rn is called a proper cone if it satisfies the following: • K is convex. • K is closed. • K is solid, which means it has nonempty interior. • K is pointed, which means that it contains no line (or equivalently, x ∈ K, − x ∈ K =⇒ x = 0). A proper cone K can be used to define a generalized inequality, which is a partial ordering on Rn that has many of the properties of the standard ordering on R.

Download PDF sample

Convex Optimization by Stephen Boyd, Lieven Vandenberghe

by Jeff

Rated 4.38 of 5 – based on 26 votes