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A very simple SQCQP method for a class of smooth convex constrained minimization problems with nice convergence results

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Abstract

We introduce a new and very simple algorithm for a class of smooth convex constrained minimization problems which is an iterative scheme related to sequential quadratically constrained quadratic programming methods, called sequential simple quadratic method (SSQM). The computational simplicity of SSQM, which uses first-order information, makes it suitable for large scale problems. Theoretical results under standard assumptions are given proving that the whole sequence built by the algorithm converges to a solution and becomes feasible after a finite number of iterations. When in addition the objective function is strongly convex then asymptotic linear rate of convergence is established.

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Acknowledgments

The author is indebted to two anonymous referees for their careful reading of this manuscript and for their useful and constructive suggestions that have helped in improving this paper.

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Authors and Affiliations

  1. Institut Camille Jordan, University Lyon I, Lyon, France

    Alfred Auslender

  2. Department of Economics, Ecole Polytechnique, Paris, France

    Alfred Auslender

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  1. Alfred Auslender
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Correspondence to Alfred Auslender.

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Auslender, A. A very simple SQCQP method for a class of smooth convex constrained minimization problems with nice convergence results. Math. Program. 142, 349–369 (2013). https://doi.org/10.1007/s10107-012-0582-3

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  • DOI: https://doi.org/10.1007/s10107-012-0582-3

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