The Use of Pseudo-Convexity and Quasi-Convexity in Sufficient Conditions for Global Constrained Extrema PDF Download
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Author: Pierre Mereau
Publisher:
ISBN:
Category :
Languages : en
Pages : 9
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Book Description
Several sufficient conditions for global constrained minima are given. These conditions consist of necessary conditions for local minima together with generalized convexity assumptions. The convexity-type assumptions are made on the Lagrangian function, which presents the advantage of not requiring any (generalized convexity) assumption on each function involved in the problem and of allowing probelms with several local extrema. Previously obtained results are used to replace pseudo-convexity by a more workable condition. (Author).
Author: Pierre Mereau
Publisher:
ISBN:
Category :
Languages : en
Pages : 9
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Book Description
Several sufficient conditions for global constrained minima are given. These conditions consist of necessary conditions for local minima together with generalized convexity assumptions. The convexity-type assumptions are made on the Lagrangian function, which presents the advantage of not requiring any (generalized convexity) assumption on each function involved in the problem and of allowing probelms with several local extrema. Previously obtained results are used to replace pseudo-convexity by a more workable condition. (Author).
Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 592
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Book Description
Author: Mokhtar S. Bazaraa
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 584
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Book Description
Convex analysis; convex sets; convex functions; optimality conditions and duality; the Fritz John and Kuhn-Tucker optimality conditions; constraint qualifications; lagrangian duality and saddle point optimality conditions; algorithms and their convergence; the concept of an algorithm; unconstrained optimization; penalty and Barrier functions; methods of feasible directions; linear complementarity, and quadratic, separable, and fractional programming; mathematical review; summary of convexity, optimality conditions, and duality.
Author: Prahba Gaiha
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
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Book Description
Recent works of Martos, Cottle and Ferland, on giving matrix theoretic criteria for the quasi-convexity and pseudo-convexity of quadratic functions over the nonnegative orthant are extended to giving necessary and sufficient conditions for a quadratic function to be quasi-convex and pseudo-convex over an arbitrary self-dual cone in E sup n, with non-empty interior. (Author).
Author: Lars Hörmander
Publisher: Birkhauser
ISBN: 0817637990
Category : Mathematics
Languages : en
Pages : 414
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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, leading up to TrA(c)preaua (TM)s theorem on sufficiency of condition (capital Greek letter Psi) for microlocal solvability in the analytic category. At the beginning of the book, no prerequisites are assumed beyond calculus and linear algebra. Later on, basic facts from distribution theory and functional analysis are needed. In a few places, a more extensive background in differential geometry or pseudodifferential calculus is required, but these sections can be bypassed with no loss of continuity. The major part of the book should therefore be accessible to graduate students so that it can serve as an introduction to complex analysis in one and several variables. The last sections, however, are written mainly for readers familiar with microlocal analysis.
Author: Olvi L. Mangasarian
Publisher:
ISBN:
Category : Convex functions
Languages : en
Pages : 17
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Book Description
A number of recent results which establish the convexity, pseudo-convexity or quasi-convexity of certain functions are shown to be special cases of the fact that under suitable conditions a composite function is convex, pseudo-convex or quasi-convex. (Author).
Author: Nicolas Hadjisavvas
Publisher: Springer Science & Business Media
ISBN: 0387233938
Category : Mathematics
Languages : en
Pages : 684
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Book Description
Studies in generalized convexity and generalized monotonicity have significantly increased during the last two decades. Researchers with very diverse backgrounds such as mathematical programming, optimization theory, convex analysis, nonlinear analysis, nonsmooth analysis, linear algebra, probability theory, variational inequalities, game theory, economic theory, engineering, management science, equilibrium analysis, for example are attracted to this fast growing field of study. Such enormous research activity is partially due to the discovery of a rich, elegant and deep theory which provides a basis for interesting existing and potential applications in different disciplines. The handbook offers an advanced and broad overview of the current state of the field. It contains fourteen chapters written by the leading experts on the respective subject; eight on generalized convexity and the remaining six on generalized monotonicity.
Author: Hoang Tuy
Publisher: Springer Science & Business Media
ISBN: 1475728093
Category : Mathematics
Languages : en
Pages : 346
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Book Description
Due to the general complementary convex structure underlying most nonconvex optimization problems encountered in applications, convex analysis plays an essential role in the development of global optimization methods. This book develops a coherent and rigorous theory of deterministic global optimization from this point of view. Part I constitutes an introduction to convex analysis, with an emphasis on concepts, properties and results particularly needed for global optimization, including those pertaining to the complementary convex structure. Part II presents the foundation and application of global search principles such as partitioning and cutting, outer and inner approximation, and decomposition to general global optimization problems and to problems with a low-rank nonconvex structure as well as quadratic problems. Much new material is offered, aside from a rigorous mathematical development. Audience: The book is written as a text for graduate students in engineering, mathematics, operations research, computer science and other disciplines dealing with optimization theory. It is also addressed to all scientists in various fields who are interested in mathematical optimization.
Author: Henryk Górecki
Publisher: Springer
ISBN: 3319626469
Category : Technology & Engineering
Languages : en
Pages : 679
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Book Description
This book offers a comprehensive presentation of optimization and polyoptimization methods. The examples included are taken from various domains: mechanics, electrical engineering, economy, informatics, and automatic control, making the book especially attractive. With the motto “from general abstraction to practical examples,” it presents the theory and applications of optimization step by step, from the function of one variable and functions of many variables with constraints, to infinite dimensional problems (calculus of variations), a continuation of which are optimization methods of dynamical systems, that is, dynamic programming and the maximum principle, and finishing with polyoptimization methods. It includes numerous practical examples, e.g., optimization of hierarchical systems, optimization of time-delay systems, rocket stabilization modeled by balancing a stick on a finger, a simplified version of the journey to the moon, optimization of hybrid systems and of the electrical long transmission line, analytical determination of extremal errors in dynamical systems of the rth order, multicriteria optimization with safety margins (the skeleton method), and ending with a dynamic model of bicycle. The book is aimed at readers who wish to study modern optimization methods, from problem formulation and proofs to practical applications illustrated by inspiring concrete examples.
Author: Jean-Pierre Crouzeix
Publisher: Springer
ISBN: 9780792350880
Category : Mathematics
Languages : en
Pages : 471
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Book Description
A function is convex if its epigraph is convex. This geometrical structure has very strong implications in terms of continuity and differentiability. Separation theorems lead to optimality conditions and duality for convex problems. A function is quasiconvex if its lower level sets are convex. Here again, the geo metrical structure of the level sets implies some continuity and differentiability properties for quasiconvex functions. Optimality conditions and duality can be derived for optimization problems involving such functions as well. Over a period of about fifty years, quasiconvex and other generalized convex functions have been considered in a variety of fields including economies, man agement science, engineering, probability and applied sciences in accordance with the need of particular applications. During the last twenty-five years, an increase of research activities in this field has been witnessed. More recently generalized monotonicity of maps has been studied. It relates to generalized convexity off unctions as monotonicity relates to convexity. Generalized monotonicity plays a role in variational inequality problems, complementarity problems and more generally, in equilibrium prob lems.
