Numerica : a modeling language for global optimization
著者
書誌事項
Numerica : a modeling language for global optimization
MIT Press, c1997
- pbk. : alk. paper
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注記
Includes bibliographical references (p. [203]-206) and index
内容説明・目次
内容説明
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.
目次
- 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.
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