Indefinite multi-constrained separable quadratic optimization: Large-scale efficient solution

Chanaka Edirisinghe

doi:10.1016/j.ejor.2019.04.004

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Indefinite multi-constrained separable quadratic optimization: Large-scale efficient solution

2019-10-01

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Chanaka Edirisinghe *

Jaehwan Jeong

DOI：10.1016/j.ejor.2019.04.004

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Abstract

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Multi-constrained indefinite separable quadratic optimization occurs in many practical applications. However, it is an NP-hard problem and its solution even for problems of moderate size is computationally tedious. Extending our previous work on singly constrained problems, we develop the necessary theory and computational procedures for problems with multiple linear constraints, by employing iterative constraint aggregation, known as surrogation. The surrogate dual solution is obtained using a cutting plane technique over the multiplier search space, which then is used to develop a monotonic sequence of upper bounds that yields a near-global optimal solution. A detailed numerical analysis indicates the method is extremely efficient for quadratic programs with hundreds of thousands of variables. While the number of constraints affects the computational efficiency, it is still an order of magnitude superior, both in speed and quality, compared to leading commercial global optimization software. Preliminary results with application to mixed integer quadratic indefinite optimization further reveal the performance superiority of the proposed methodology relative to the standard techniques. (C) 2019 Elsevier B.V. All rights reserved.

Keywords:

Nonlinear programming

Large scale optimization

Integer programming

Global optimization

Constraint aggregation

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