Generalized Polynomial Programming

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Generalized Polynomial Programming

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Author : Gary Edmund Blau
language : en
Publisher:
Release Date : 1967

Generalized Polynomial Programming written by Gary Edmund Blau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Programming (Mathematics) categories.

A Primal Dual Algorithm For Constrained Generalized Polynomial Programming

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Author : Alice M. Agogino
language : en
Publisher:
Release Date : 1984

A Primal Dual Algorithm For Constrained Generalized Polynomial Programming written by Alice M. Agogino and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Algorithms categories.

Some Applications Of Generalized Polynomial Programming To Chemical Process Problems

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Author : Richard Lee Sleeter
language : en
Publisher:
Release Date : 1969

Some Applications Of Generalized Polynomial Programming To Chemical Process Problems written by Richard Lee Sleeter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Chemical processes categories.

An Application Of Generalized Polynomial Programming And The Modified Method Of Multiplier In Preliminary Chemical Process Design

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Author : Fu-chuan Thomas Lee
language : en
Publisher:
Release Date : 1983

An Application Of Generalized Polynomial Programming And The Modified Method Of Multiplier In Preliminary Chemical Process Design written by Fu-chuan Thomas Lee and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.

A Program For Manipulating And Solving Nonlinear Generalized Polynomial Optimization Problems With Geometric Programming And Symbolic Constraint Reduction

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Author : David C. Ketchum
language : en
Publisher:
Release Date : 1996

A Program For Manipulating And Solving Nonlinear Generalized Polynomial Optimization Problems With Geometric Programming And Symbolic Constraint Reduction written by David C. Ketchum and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Geometric programming categories.

Computing Generalized Nash Equilibria By Polynomial Programming

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Author : Philipp Renner
language : en
Publisher:
Release Date : 2014

Computing Generalized Nash Equilibria By Polynomial Programming written by Philipp Renner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.

We present a new way to solve generalized Nash equilibrium problems. We assume the feasible set to be compact. Furthermore all functions are assumed to be polynomials. However we do not need any convexity assumptions on either the utility functions or the action sets. The key idea is to use Putinar's Positivstellensatz, a representation result for positive polynomials, to replace each agent's problem by a convex optimization problem. The Nash equilibria are then feasible solutions to a system of polynomial equations and inequalities. Our application is a model of the New Zealand electricity spot market with transmission losses based on a real dataset.

Advances In Geometric Programming

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Author : Mordecai Avriel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Advances In Geometric Programming written by Mordecai Avriel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

In 1961, C. Zener, then Director of Science at Westinghouse Corpora tion, and a member of the U. S. National Academy of Sciences who has made important contributions to physics and engineering, published a short article in the Proceedings of the National Academy of Sciences entitled" A Mathe matical Aid in Optimizing Engineering Design. " In this article Zener considered the problem of finding an optimal engineering design that can often be expressed as the problem of minimizing a numerical cost function, termed a "generalized polynomial," consisting of a sum of terms, where each term is a product of a positive constant and the design variables, raised to arbitrary powers. He observed that if the number of terms exceeds the number of variables by one, the optimal values of the design variables can be easily found by solving a set of linear equations. Furthermore, certain invariances of the relative contribution of each term to the total cost can be deduced. The mathematical intricacies in Zener's method soon raised the curiosity of R. J. Duffin, the distinguished mathematician from Carnegie Mellon University who joined forces with Zener in laying the rigorous mathematical foundations of optimizing generalized polynomials. Interes tingly, the investigation of optimality conditions and properties of the optimal solutions in such problems were carried out by Duffin and Zener with the aid of inequalities, rather than the more common approach of the Kuhn-Tucker theory.

Global Optimization Of Nonconvex Generalized Polynomial Design Models Design

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Author : CHIHSIUNG LO
language : en
Publisher:
Release Date : 1991

Global Optimization Of Nonconvex Generalized Polynomial Design Models Design written by CHIHSIUNG LO and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Automatic control categories.

other hand, most deterministic algorithms are restricted to certain classes of problems. In this dissertation, a deterministic approach is investigated for a special class of problems called generalized polynomial problems which occur often in engineering applications.

Nondifferentiable Optimization And Polynomial Problems

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Author : N.Z. Shor
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Nondifferentiable Optimization And Polynomial Problems written by N.Z. Shor and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

Polynomial extremal problems (PEP) constitute one of the most important subclasses of nonlinear programming models. Their distinctive feature is that an objective function and constraints can be expressed by polynomial functions in one or several variables. Let :e = {:e 1, ... , :en} be the vector in n-dimensional real linear space Rn; n PO(:e), PI (:e), ... , Pm (:e) are polynomial functions in R with real coefficients. In general, a PEP can be formulated in the following form: (0.1) find r = inf Po(:e) subject to constraints (0.2) Pi (:e) =0, i=l, ... ,m (a constraint in the form of inequality can be written in the form of equality by introducing a new variable: for example, P( x) ~ 0 is equivalent to P(:e) + y2 = 0). Boolean and mixed polynomial problems can be written in usual form by adding for each boolean variable z the equality: Z2 - Z = O. Let a = {al, ... ,a } be integer vector with nonnegative entries {a;}f=l. n Denote by R[a](:e) monomial in n variables of the form: n R[a](:e) = IT :ef'; ;=1 d(a) = 2:7=1 ai is the total degree of monomial R[a]. Each polynomial in n variables can be written as sum of monomials with nonzero coefficients: P(:e) = L caR[a](:e), aEA{P) IX x Nondifferentiable optimization and polynomial problems where A(P) is the set of monomials contained in polynomial P.

Interior Point Polynomial Algorithms In Convex Programming

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Author : Yurii Nesterov
language : en
Publisher: SIAM
Release Date : 1987-01-01

Interior Point Polynomial Algorithms In Convex Programming written by Yurii Nesterov and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-01-01 with Mathematics categories.

Written for specialists working in optimization, mathematical programming, or control theory. The general theory of path-following and potential reduction interior point polynomial time methods, interior point methods, interior point methods for linear and quadratic programming, polynomial time methods for nonlinear convex programming, efficient computation methods for control problems and variational inequalities, and acceleration of path-following methods are covered. In this book, the authors describe the first unified theory of polynomial-time interior-point methods. Their approach provides a simple and elegant framework in which all known polynomial-time interior-point methods can be explained and analyzed; this approach yields polynomial-time interior-point methods for a wide variety of problems beyond the traditional linear and quadratic programs.