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Bridging the gap between Trust–Region Methods (TRMs) and Linesearch Based Methods (LBMs) for Nonlinear Programming: quadratic sub–problems

Author

Listed:
  • Giovanni Fasano

    (Dept. of Management, Università Ca' Foscari Venice)

  • Christian Piermarini

    (Dept. of Computer, Control and Management Engineering, Sapienza University of Rome)

  • Massimo Roma

    (Dept. of Computer, Control and Management Engineering, Sapienza University of Rome)

Abstract

We consider the solution of a recurrent sub–problem within both constrained and unconstrained Nonlinear Programming: namely the minimization of a quadratic function subject to linear constraints. This problem appears in a number of LBM frameworks, and to some extent it reveals a close analogy with the solution of trust–region sub–problems. In particular, we refer to a structured quadratic problem where five linear inequality constraints are included. We show that our proposal retains an appreciable versatility, despite its particular structure, so that a number of different real instances may be reformulated following the pattern in our proposal. Moreover, we detail how to compute an exact global solution of our quadratic sub–problem, exploiting first order KKT conditions.

Suggested Citation

  • Giovanni Fasano & Christian Piermarini & Massimo Roma, 2022. "Bridging the gap between Trust–Region Methods (TRMs) and Linesearch Based Methods (LBMs) for Nonlinear Programming: quadratic sub–problems," Working Papers 08, Venice School of Management - Department of Management, Università Ca' Foscari Venezia.
    • Handle: RePEc:vnm:wpdman:194
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    More about this item

    Keywords

    Nonlinear Programming; Quadratic linearly constrained problems; KKT conditions;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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