Ten years ago, the broad consensus among researchers in constrained optimization was that sequential quadratic programming (SQP) methods were the methods of choice. While, in the long term, this position may be justiied, the past ten years have exposed a number of diiculties with the SQP approach. Moreover, alternative methods have shown themselves capable of solving large-scale problems. In th...

Introduction Since its popularization in the late s Sequential Quadratic Program ming SQP has arguably become the most successful method for solving nonlinearly constrained optimization problems As with most optimization methods SQP is not a single algorithm but rather a conceptual method from which numerous speci c algorithms have evolved Backed by a solid theoretical and computational foundat...

We consider solving nonlinear optimization problems with a stochastic objective and deterministic equality constraints. assume for the that its evaluation, gradient, Hessian are inaccessible, while one can compute their estimates by, example, subsampling. propose algorithm based on sequential quadratic programming (SQP) uses differentiable exact augmented Lagrangian as merit function. To motiva...

As is well known, Q-superlinear or Q-quadratic convergence of the primal-dual sequence generated by an optimization algorithm does not, in general, imply Q-superlinear convergence of the primal part. Primal convergence, however, is often of particular interest. For the sequential quadratic programming (SQP) algorithm, local primal-dual quadratic convergence can be established under the assumpti...

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We propose an SQP algorithm for mathematical programs with vanishing constraints which solves at each iteration a quadratic program with linear vanishing constraints. The algorithm is based on the newly developed concept of [Formula: see text]-stationarity (Benko and Gfrerer in Optimization 66(1):61-92, 2017). We demonstrate how [Formula: see text]-stationary solutions of the quadratic program ...

In this paper we develop an algorithm for solving a version of the (static) traac equilibrium problem in which the cost incurred on each path is not simply the sum of the costs on the arcs that constitute that path. The method we describe is based on the recent NE/SQP algorithm , a fast and robust technique for solving nonlinear complementarity problems. Finally, we present an example that illu...

In this paper we present a version of the (static) traac equilibrium problem in which the cost incurred on a path is not simply the sum of the costs on the arcs that constitute that path. We motivate this nonadditive version of the problem by describing several situations in which the classical additiv-ity assumption fails. We also present an algorithm for solving nonadditive problems that is b...

A graph is a strict-quasi parity (SQP) graph if every induced subgraph that is not a clique contains a pair of vertices with no odd chordless path between them (an``even pair''). We present an O…n 3 † algorithm for recognizing planar strict quasi-parity graphs, based on Wen-Lian Hsu's decomposition of planar (perfect) graphs and on the (non-algorithmic) characterization of planar minimal non-SQ...