Linearly constrained global optimization via piecewise-linear approximation

This paper considers the problem of optimizing a continuous nonlinear objective function subject to linear constraints via a piecewise-linear approximation. A systematic approach is proposed, which uses a lattice piecewise-linear model to approximate the nonlinear objective function on a simplicial...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 214; no. 1; pp. 111 - 120
Main Authors Zhang, Hao, Wang, Shuning
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 15.04.2008
Elsevier
Subjects
Calculus of variations and optimal control
Combinatorics. Ordered structures
Exact sciences and technology
Global optimization
Lattice piecewise-linear model
Mathematical analysis
Mathematics
Nonlinear programming
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Order, lattices, ordered algebraic structures
Piecewise-linear approximation
Real functions
Sciences and techniques of general use
Global optimization
90C30
65K05
Piecewise-linear approximation
65D15
Nonlinear programming
Lattice piecewise-linear model
Partition
Global optimization; Piecewise-linear approximation; Lattice piecewise-linear model; Nonlinear programming
Optimization method
Continuous function
Nonlinear problems
Non linear programming
Linear model
Constrained optimization
Numerical analysis
Applied mathematics
Linear approximation
Non linear model
Optimal solution
90C30; 65K05; 65D15
Mathematical programming
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ISSN0377-0427
1879-1778
DOI10.1016/j.cam.2007.02.006

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Summary:This paper considers the problem of optimizing a continuous nonlinear objective function subject to linear constraints via a piecewise-linear approximation. A systematic approach is proposed, which uses a lattice piecewise-linear model to approximate the nonlinear objective function on a simplicial partition and determines an approximately globally optimal solution by solving a set of standard linear programs. The new approach is applicable to any continuous objective function rather than to separable ones only and could be useful to treat more complex nonlinear problems. A numerical example is given to illustrate the practicability.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2007.02.006