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A SUPERLINEARLY CONVERGENT ALGORITHM FOR LARGE SCALE MULTI-STAGE STOCHASTIC NONLINEAR PROGRAMMING

Centre for Industrial Mathematics and Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Singapore

Current affiliation: School of Mathematics, University of Southampton, Highfield Southampton, SO17 1BJ, UK.

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ROGER C. E. TAN

Centre for Industrial Mathematics and Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Singapore

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, and

GONGYUN ZHAO

Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Singapore

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https://doi.org/10.1142/S1465876304002411Cited by:2 (Source: Crossref)

Abstract

This paper presents an algorithm for solving a class of large scale nonlinear programming which is originally derived from the multi-stage stochastic convex nonlinear programming. With the Lagrangian-dual method and the Moreau-Yosida regularization, the primal problem is transformed into a smooth convex problem. By introducing a self-concordant barrier function, an approximate generalized Newton method is designed in this paper. The algorithm is shown to be of superlinear convergence. At last, some preliminary numerical results are provided.

Keywords:

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