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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.

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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