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A General Regularized Continuous Formulation for the Maximum Clique Problem

James T. Hungerford(jamesthungerford***at***gmail.com )
Francesco Rinaldi(rinaldi***at***math.unipd.it)

Abstract: In this paper, we develop a general regularization-based continuous optimization framework for the maximum clique problem. In particular, we consider a broad class of regularization terms that can be included in the classic Motzkin-Strauss formulation and we develop conditions that guarantee the equivalence between the continuous regularized problem and the original one in both a global and a local sense. We further analyze, from a computational point of view, two different regularizers that satisfy the general conditions.

Keywords: Maximum clique, sparse optimization, support, concave mini- mization, Motzkin-Straus

Category 1: Combinatorial Optimization

Category 2: Nonlinear Optimization

Category 3: Network Optimization


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Entry Submitted: 09/11/2017
Entry Accepted: 09/13/2017
Entry Last Modified: 09/11/2017

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