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A gradient descent based algorithm for lp minimization
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DOI：10.1016/j.ejor.2019.11.051.png)
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Abstract
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In this paper, we study the linearly constrained l(p) minimization problem with p is an element of (0, 1). Unlike those known works in the literature that propose solving relaxed epsilon-KKT conditions, we introduce a scaled KKT condition without involving any relaxation of the optimality conditions. A gradient-descent-based algorithm that works only on the positive entries of variables is then proposed to find solutions satisfying the scaled KKT condition without invoking the nondifferentiability issue. The convergence proof and complexity analysis of the proposed algorithm are provided. Computational experiments support that the proposed algorithm is capable of achieving much better sparse recovery in reasonable computational time compared to state-of-the-art interior-point based algorithms. (C) 2019 Elsevier B.V. All rights reserved.
Keywords:
Global optimization
Nonsmooth optimization
Nonconvex optimization
Gradient descent algorithm
KKT condition
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