Maximal Domains of Quasi-convexity and Pseudo-convexity for Quadratic Functions PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Maximal Domains of Quasi-convexity and Pseudo-convexity for Quadratic Functions PDF full book. Access full book title Maximal Domains of Quasi-convexity and Pseudo-convexity for Quadratic Functions by Jacques A. Ferland. Download full books in PDF and EPUB format.
Author: Jacques A. Ferland
Publisher:
ISBN:
Category :
Languages : en
Pages : 74
Get Book Here
Book Description
Author: Jacques A. Ferland
Publisher:
ISBN:
Category :
Languages : en
Pages : 74
Get Book Here
Book Description
Author: Jacques A. Ferland
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 84
Get Book Here
Book Description
The purpose of the paper is to prove that testing quasi-convexity (pseudo-convexity) of quadratic functions on solid convex sets can be reduced to an examination of finitely many conditions. One determines two maximal domains of quasi-convexity (pseudo-convexity) for the quadratic form Psi(x) = (x, Dx) where D has exactly one negative eigenvalue, and conversely, one shows that if the quadratic form Psi is quasi-convex (pseudo-convex) on a solid convex set, then the matrix D has exactly one negative eignevalue and the solid convex set is contained in one of the maximal domains. The special case when the solid convex set is the nonnegative (semi-positive) orthant is also analyzed. This study is then extended to quadratic functions Phi(x) = 1/2(x, Dx) + (c, x). Analogous results hold under the additional condition that the set (a/Da+c = 0) is not empty. In the last part of this paper, one analyzes functions that are not necessarily quadratic. One obtains some results on mathematical programming problems having twice differentiable quasi-convex objective function and constraint functions. Finally, one gives a necessary condition and a sufficient condition for the quasi-convexity of a function in Class C squared (i.e., twice continuously differentiable) on a solid convex set. One also establishes a relation between the quasi-convexity and the pseudo-convexity of twice differentiable functions on solid convex sets. (Author).
Author: Alberto Cambini
Publisher: Springer Science & Business Media
ISBN: 3540708766
Category : Mathematics
Languages : en
Pages : 252
Get Book Here
Book Description
The authors have written a rigorous yet elementary and self-contained book to present, in a unified framework, generalized convex functions. The book also includes numerous exercises and two appendices which list the findings consulted.
Author: Mordecai Avriel
Publisher: SIAM
ISBN: 0898718961
Category : Mathematics
Languages : en
Pages : 342
Get Book Here
Book Description
Originally published: New York: Plenum Press, 1988.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 436
Get Book Here
Book Description
Author: Stanford University. Department of Operations Research
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
Get Book Here
Book Description
Second order characterizations for (strictly) pseudoconvex functions are derived in terms of extended Hessians and bordered determinants. Additional results are presented for quadratic functions. (Author).
Author: Lars Hörmander
Publisher: Springer Science & Business Media
ISBN: 0817645853
Category : Mathematics
Languages : en
Pages : 424
Get Book Here
Book Description
The first two chapters of this book are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the study in the following chapters of related notions which occur in the theory of linear partial differential equations and complex analysis such as (pluri-)subharmonic functions, pseudoconvex sets, and sets which are convex for supports or singular supports with respect to a differential operator. In addition, the convexity conditions which are relevant for local or global existence of holomorphic differential equations are discussed.
Author: Giorgio Giorgi
Publisher: Elsevier
ISBN: 008053595X
Category : Mathematics
Languages : en
Pages : 615
Get Book Here
Book Description
The book is intended for people (graduates, researchers, but also undergraduates with a good mathematical background) involved in the study of (static) optimization problems (in finite-dimensional spaces). It contains a lot of material, from basic tools of convex analysis to optimality conditions for smooth optimization problems, for non smooth optimization problems and for vector optimization problems.The development of the subjects are self-contained and the bibliographical references are usually treated in different books (only a few books on optimization theory deal also with vector problems), so the book can be a starting point for further readings in a more specialized literature.Assuming only a good (even if not advanced) knowledge of mathematical analysis and linear algebra, this book presents various aspects of the mathematical theory in optimization problems. The treatment is performed in finite-dimensional spaces and with no regard to algorithmic questions. After two chapters concerning, respectively, introductory subjects and basic tools and concepts of convex analysis, the book treats extensively mathematical programming problems in the smmoth case, in the nonsmooth case and finally vector optimization problems.· Self-contained· Clear style and results are either proved or stated precisely with adequate references· The authors have several years experience in this field· Several subjects (some of them non usual in books of this kind) in one single book, including nonsmooth optimization and vector optimization problems· Useful long references list at the end of each chapter
Author: Jacques A. Ferland
Publisher:
ISBN:
Category :
Languages : en
Pages : 18
Get Book Here
Book Description
Author: R. B. Bapat
Publisher: Cambridge University Press
ISBN: 0521571677
Category : Mathematics
Languages : en
Pages : 351
Get Book Here
Book Description
This book provides an integrated treatment of the theory of nonnegative matrices (matrices with only positive numbers or zero as entries) and some related classes of positive matrices, concentrating on connections with game theory, combinatorics, inequalities, optimisation and mathematical economics. The wide variety of applications, which include price fixing, scheduling and the fair division problem, have been carefully chosen both for their elegant mathematical content and for their accessibility to students with minimal preparation. Many results in matrix theory are also presented. The treatment is rigorous and almost all results are proved completely. These results and applications will be of great interest to researchers in linear programming, statistics and operations research. The minimal prerequisites also make the book accessible to first-year graduate students.
