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An SQP algorithm for extended linear-quadratic problems in stochastic programming

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Abstract

Extended Linear-Quadratic Programming (ELQP) problems were introduced by Rockafellar and Wets for various models in stochastic programming and multistage optimization. Several numerical methods with linear convergence rates have been developed for solving fully quadratic ELQP problems, where the primal and dual coefficient matrices are positive definite. We present a two-stage sequential quadratic programming (SQP) method for solving ELQP problems arising in stochastic programming. The first stage algorithm realizes global convergence and the second stage algorithm realizes superlinear local convergence under a condition calledB-regularity.B-regularity is milder than the fully quadratic condition; the primal coefficient matrix need not be positive definite. Numerical tests are given to demonstrate the efficiency of the algorithm. Solution properties of the ELQP problem underB-regularity are also discussed.

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Authors and Affiliations

  1. School of Mathematics, University of New South Wales, 2033, Kensington, N.S.W., Australia

    Liqun Qi & Robert S. Womersley

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  1. Liqun Qi
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  2. Robert S. Womersley
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Supported by the Australian Research Council.

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Qi, L., Womersley, R.S. An SQP algorithm for extended linear-quadratic problems in stochastic programming. Ann Oper Res 56, 251–285 (1995). https://doi.org/10.1007/BF02031711

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