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Abstract: In this paper, we present a general algorithm for nonlinear programming which uses a slanting filter criterion for accepting the new iterates. Independently of how these iterates are computed, we prove that all accumulation points of the sequence generated by the algorithm are feasible. Computing the new iterates by the inexact restoration method, we prove stationarity of all accumulation points of the sequence. [Copyright &y& Elsevier]

The long-term operation of hydro-thermal power generation systems is modeled by a large-scale stochastic optimization problem that includes nonlinear constraints due to the head computation in hydroelectric plants. We do a detailed development of the problem model and state it by a non-anticipative scenario analysis, leading to a large-scale nonlinear programming problem. This is solved by a filter algorithm with sequential quadratic programming iterations that minimize quadratic Lagrangian approximations using exact hessians in L ∞ trust regions. The method is applied to the long-term planning of the Brazilian system, with over 100 hydroelectric and 50 thermoelectric plants, distributed in 5 interconnected subsystems. This problem with 50 synthetically generated inflow scenarios and a horizon of 60 months, amounting to about one million variables and 15000 nonlinear constraints was solved by the filter algorithm in a standard 2016 notebook computer in 10 h of CPU. [ABSTRACT FROM AUTHOR]

Abstract: In this work we discuss global convergence of a general filter algorithm that depends neither on the definition of the forbidden region, which can be given by the original or slanting filter rule, nor on the way in which the step is computed. This algorithm basically consists of calculating a point not forbidden by the filter from the current point. Assuming that this step must be efficient, in the sense that near a feasible non-stationary point the decrease in the objective function is relatively large, we prove the global convergence of the algorithm. We also discuss that such a condition is satisfied if the step is computed by the SQP or Inexact Restoration methods. For SQP we present a general proof of this result that is valid for both the original and the slanting filter criterion. In order to compare the performance of the general filter algorithm according to the method used to calculate the step and the filter rule regarded, we present numerical experiments performed with problems from CUTEr collection. [Copyright &y& Elsevier]