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A filter method with unified step computation for nonlinear optimization. (English) Zbl 1301.49070
In this paper, the authors present a filter line search method for solving general nonlinear and nonconvex optimization problems. They replace the traditional restoration phase with an exact penalty function to compute a search direction. Each search direction is defined as a convex combination of a steering step (a solution of a linear program) that represents the best local improvement in constraint violation and a predictor step that reduces their strictly convex quadratic model of the exact penalty function. Under standard assumptions they prove global convergence of their algorithm.

MSC:
49M05 Numerical methods based on necessary conditions
49M15 Newton-type methods
65K05 Numerical mathematical programming methods
65K10 Numerical optimization and variational techniques
90C55 Methods of successive quadratic programming type
90C30 Nonlinear programming
90C26 Nonconvex programming, global optimization
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