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A Barrier Method for Large-Scale Constrained Optimization
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1993
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Numerical AnalysisMathematical ProgrammingLarge-scale Global OptimizationEngineeringInequality ConstraintsNonlinear ProgrammingConvex OptimizationComputer EngineeringConstrained OptimizationLogarithmic Barrier MethodComputer ScienceNonlinear OptimizationLinear ProgrammingUnconstrained OptimizationApproximation TheoryBarrier MethodBarrier MethodsOperations Research
A logarithmic barrier method is applied to the solution of a nonlinear programming problem with inequality constraints. An approximation to the Newton direction is derived that avoids the ill conditioning normally associated with barrier methods. This approximation can be used within a truncated-Newton method, and hence is suitable for large-scale problems; the approximation can also be used in the context of a parallel algorithm. Enhancements to the basic barrier method are described that improve its efficiency and reliability. The resulting method can be shown to be a primal-dual method when the objective function is convex and all of the constraints are linear. Computational experiments are presented where the method is applied to 1000-variable problems with bound constraints. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.