Constrained global optimization: algorithms and applications
Global optimization is concerned with the characterization and computation of global minima or maxima of nonlinear functions. Such problems are widespread in mathematical modeling of real world systems for a very broad range of applications. The applications include economies of scale, fixed charges, allocation and location problems, quadratic assignment and a number of other combinatorial optimization problems. More recently it has been shown that certain aspects of VLSI chip design and database problems can be formulated as constrained global optimization problems with a quadratic objective function. Although standard nonlinear programming algorithms will usually obtain a local minimum to the problem, such a local minimum will only be global when certain conditions are satisfied (such as "f" and "K" being convex).
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Convex sets and functions
Combinatorial optimization problems that can be formu
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Constrained Global Optimization: Algorithms and Applications
Panos M. Pardalos,J. Ben Rosen
No preview available - 2014
approximate solution bilinear bounded polyhedron branch and bound concave cost concave function concave minimization problem concave programming concave quadratic cone convergence convex envelope convex function convex set convex underestimating cutting plane method defined equivalent extreme points Falk feasible domain finite formulated function value global minimum global optimization global solution Horst indefinite quadratic problem integer linear program integer program KT conditions linear complementarity problem linear constraints linear function linear problem linear programming problem linear underestimating function linearly lower bound Math mathematical programming Minimum concave mixed integer nonconvex programming problems nonconvex quadratic nonlinear programming objective function obtain Oper optimal solution optimum original problem Pardalos partition piecewise linear approximation polyhedral set polytope Progr Proof quadratic assignment problem quadratic function quadratic programming ranking the extreme rectangle Rosen simplex subproblems symmetric matrix test problems Theorem tion Tuy's Univ upper bounds variables vector vertex xeRn zero-one integer