A study on sequential minimal optimization methods for standard quadratic problems

Riccardo Bisori, Matteo Lapucci () and Marco Sciandrone
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Riccardo Bisori: Università degli Studi di Firenze
Matteo Lapucci: Università degli Studi di Firenze
Marco Sciandrone: Università degli Studi di Firenze

4OR, 2022, vol. 20, issue 4, No 5, 685-712

Abstract: Abstract In this work, we consider the relevant class of Standard Quadratic Programming problems and we propose a simple and quick decomposition algorithm, which sequentially updates, at each iteration, two variables chosen by a suitable selection rule. The main features of the algorithm are the following: (1) the two variables are updated by solving a subproblem that, although nonconvex, can be analytically solved; (2) the adopted selection rule guarantees convergence towards stationary points of the problem. Then, the proposed Sequential Minimal Optimization algorithm, which optimizes the smallest possible sub-problem at each step, can be used as efficient local solver within a global optimization strategy. We performed extensive computational experiments and the obtained results show that the proposed decomposition algorithm, equipped with a simple multi-start strategy, is a valuable alternative to the state-of-the-art algorithms for Standard Quadratic Optimization Problems.

Date: 2022
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DOI: 10.1007/s10288-021-00496-9

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