Solution of boolean quadratic programming problems by two augmented Lagrangian algorithms based on a continuous relaxation

Rupaj Kumar Nayak () and Nirmalya Kumar Mohanty ()
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Rupaj Kumar Nayak: International Institute of Information Technology
Nirmalya Kumar Mohanty: International Institute of Information Technology

Journal of Combinatorial Optimization, 2020, vol. 39, issue 3, No 9, 792-825

Abstract: Abstract Many combinatorial optimization problems and engineering problems can be modeled as boolean quadratic programming (BQP) problems. In this paper, two augmented Lagrangian methods (ALM) are discussed for the solution of BQP problems based on a class of continuous functions. After convexification, the BQP is reformulated as an equivalent augmented Lagrangian function, and then solved by two ALM algorithms. Within this ALM algorithm, L-BFGS is called for the solution of unconstrained nonlinear programming problem. Experiments are performed on max-cut problem, 0–1 quadratic knapsack problem and image deconvolution, which indicate that ALM method is promising for solving large scale BQP by the quality of near optimal solution with low computational time.

Keywords: Binary quadratic programming problem; Continuous relaxation; Augmented Lagrangian method; Max-cut problems; QKP; Image deconvolution (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10878-019-00517-8

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