A quadratic penalty method for hypergraph matching

Chunfeng Cui (), Qingna Li (), Liqun Qi () and Hong Yan ()
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Chunfeng Cui: City University of Hong Kong
Qingna Li: Beijing Institute of Technology
Liqun Qi: The Hong Kong Polytechnic University
Hong Yan: City University of Hong Kong

Journal of Global Optimization, 2018, vol. 70, issue 1, No 13, 237-259

Abstract: Abstract Hypergraph matching is a fundamental problem in computer vision. Mathematically, it maximizes a polynomial objective function, subject to assignment constraints. In this paper, we reformulate the hypergraph matching problem as a sparse constrained optimization problem. By dropping the sparse constraint, we show that the resulting relaxation problem can recover the global minimizer of the original problem. This property heavily depends on the special structures of hypergraph matching. The critical step in solving the original problem is to identify the location of nonzero entries (referred to as the support set) in a global minimizer. Inspired by such observation, we apply the quadratic penalty method to solve the relaxation problem. Under reasonable assumptions, we show that the support set of the global minimizer in a hypergraph matching problem can be correctly identified when the number of iterations is sufficiently large. A projected gradient method is applied as a subsolver to solve the quadratic penalty subproblem. Numerical results demonstrate that the exact recovery of the support set indeed happens, and the proposed algorithm is efficient in terms of both accuracy and CPU time.

Keywords: Hypergraph matching; Sparse optimization; Quadratic penalty method; Projected gradient method (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10898-017-0583-0

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