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...

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...

-Aiming at the shortcoming of basic PSO algorithm, that is, easily trapping into local minimum, we propose an advanced PSO algorithm with SA and apply this new algorithm for solving TSP problem. The core of algorithm is based on the PSO algorithm. SA method is used to slow down the degeneration of the PSO swarm and increase the swarm’s diversity. The comparative experiments were made between PS...

We present the first bioluminescence tomography algorithm that makes use of the PDEconstrained concept, which has shown to lead to significant savings in computation times in similar applications. Implementing a sequential quadratic programming (SQP) method, we solve the forward and inverse problems simultaneously. Using numerical results we show that the PDEconstrained SQP approach leads to ~1...

We present an algorithm for large-scale equality constrained optimization. The method is based on a characterization of inexact sequential quadratic programming (SQP) steps that can ensure global convergence. Inexact SQP methods are needed for large-scale applications for which the iteration matrix cannot be explicitly formed or factored and the arising linear systems must be solved using itera...

Merit functions utilized to monitor the convergence of sequential quadratic programming (SQP) methods for nonlinear programs and variational inequality problems have in common that they include a penalty function for the explicit constraints, the value of the penalty parameter for which is subject to the requirement of being large enough compared to estimates of the optimal Lagrange multipliers...