Abstract
A Sequential Quadratic Programming (in short, SQP) algorithm is presented for solving constrained nonlinear programming problems. The algorithm uses three stepsize strategies, in order to achieve global and superlinear convergence. Switching rules are implemented that combine the merits and avoid the drawbacks of the three stepsize strategies. A penalty parameter is determined, using an adaptive strategy that aims to achieve sufficient decrease of the activated merit function. Global convergence is established and it is also shown that, locally, unity step sizes are accepted. Therefore, superlinear convergence is not impeded under standard assumptions. Global convergence and convergence of the stepsizes are displayed on test problems from the Hock and Schittkowski collection.
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Communicated by P.M. Pardalos.
The authors would like to thank the anonymous referees and Prof. F. Giannessi for their useful comments.
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Tzallas-Regas, G., Rustem, B. Switching Stepsize Strategies for Sequential Quadratic Programming. J Optim Theory Appl 149, 269–292 (2011). https://doi.org/10.1007/s10957-010-9790-2
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DOI: https://doi.org/10.1007/s10957-010-9790-2