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A second-order convergence augmented Lagrangian method using non-quadratic penalty functions

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Abstract

The purpose of the present paper is to study the global convergence of a practical Augmented Lagrangian model algorithm that considers non-quadratic Penalty–Lagrangian functions. We analyze the convergence of the model algorithm to points that satisfy the Karush–Kuhn–Tucker conditions and also the weak second-order necessary optimality condition. The generation scheme of the Penalty–Lagrangian functions includes the exponential penalty function and the logarithmic-barrier without using convex information.

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Authors and Affiliations

  1. CONICET, Department of Mathematics, FCE, University of La Plata, CP 172, 1900, La Plata, Bs. As., Argentina

    M. D. Sánchez & M. L. Schuverdt

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  1. M. D. Sánchez
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  2. M. L. Schuverdt
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Correspondence to M. L. Schuverdt.

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Sánchez, M.D., Schuverdt, M.L. A second-order convergence augmented Lagrangian method using non-quadratic penalty functions. OPSEARCH 56, 390–408 (2019). https://doi.org/10.1007/s12597-019-00366-3

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