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A globally convergent primal-dual interior-point filter method for nonlinear programming. (English) Zbl 1070.90110
The paper proposes an algorithm which uses the filter technique of Fletcher and Leyffer to globalize the primal-dual interior-point method for nonlinear optimization, avoiding the use of merit functions and the updating of penalty parameters. This algorithm decomposes the primal-dual step obtained from the perturbed first-order necessary conditions into a normal and a tangential step, whose sizes are controlled by a trust-region type parameter. Each entry in the filter is a pair of coordinates: one resulting from feasibility and centrality, and associated with the normal step, the other resulting from optimality and related with the tangential step.
MSC:
90C30Nonlinear programming
90C51Interior-point methods
65K05Mathematical programming (numerical methods)
90C29Multi-objective programming; goal programming