Numerica

A Modeling Language for Global Optimization

av Pascal Van Hentenryck, Laurent Michel, Yves Deville

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(häftad)

Format:: Häftad (paperback)
Utgiven:: 1997-07-01
Språk:: Engelska

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Many science and engineering applications require the user to find solutions to systems of nonlinear constraints or to optimize a nonlinear function subject to nonlinear constraints. The field of global optimization is the study of methods to find all solutions to systems of nonlinear constraints and all global optima to optimization problems. Numerica is modeling language for global optimization that makes it possible to state nonlinear problems in a form close to the statements traditionally found in textbooks and scientific papers. The constraint-solving algorithm of Numerica is based on a combination of traditional numerical methods such as interval and local methods, and constraint satisfaction techniques.This comprehensive presentation of Numerica describes its design, functions, and implementation. It also discusses how to use Numerica effectively to solve practical problems and reports a number of experimental results.A commercial implementation of Numerica is available from ILOG under the name ILOG Numerica.

(Bookdata)

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"This book describes an exciting development in computer science. It describes a system which allows non-mathematicians to solve difficult numerical problems using interval reasoning. The advanced interval reasoning techniques used by *Numerica* enable it to handle non-linear constraints and optimization with many benefits. As such this book is of considerable interest to a wide audience." --Mark G. Wallace, IC-Parc, William Penney Laboratory, Imperial College, London

(Bookdata)

Laurent Michel is Assistant Professor in the Department of Computer Science and Engineering at the University of Connecticut.

(Bookdata)

Online Stochastic Combinatorial Optimization
Pascal Van Hentenryck, Russell Bent (inbunden)

Constraint-Based Local Search
Pascal Van Hentenryck, Laurent Michel (häftad)

Principles and Practice of Constraint Programming
Vijay A Saraswat, Pascal Van Hentenryck (häftad)

Practical Aspects of Declarative Languages
Pascal Van Hentenryck (häftad)

Part 1 Introduction: nonlinear programming; local methods; global methods; Numerica; outline. Part 2 A tour of Numerica: getting started; generic constraints; constants; ranges; input parameters; aggregation operators; functions; sets; unconstrained optimization; constrained optimization; local constraint solving; local unconstrained optimization; soft constraints; real constraints and uncertain data; display; accuracy. Part 3 The meaning of Numerica: interval analysis; constraint solving; unconstrained optimization; interpretation of the results. Part 4 Modelling in Numerica: what can go wrong in Numerica; improving Numerica statements. Part 5 The syntax of Numerica: overall structure; expressions; the constant section; the input section; the set section; the variable section; the function section; the body section; the display section; the pragma section; scoping rules. Part 6 The semantics of Numerica: interval arithmetic; semantics of constraint solving; semantics of unconstrained minimization; semantics of constrained minimization; non-canonical boxes. Part 7 An implementation of Numerica: overview of the algorithm; domain-specific and monotonic interval extensions; constraint solving; unconstrained optimization; constrained optimization; advanced techniques; an implementation of box consistency. Part 8 Experimental results: constraint solving; unconstrained optimization; constrained optimization; appendices.

(Bookdata)