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

Giovanni Fasano (), Christian Piermarini () and Massimo Roma ()
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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

No 8, Working Papers from Venice School of Management - Department of Management, Università Ca' Foscari Venezia

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.

Keywords: Nonlinear Programming; Quadratic linearly constrained problems; KKT conditions (search for similar items in EconPapers)
JEL-codes: C44 C61 (search for similar items in EconPapers)
Pages: 27 pages
Date: 2022-07
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