Smoothing projected Barzilai–Borwein method for constrained non-Lipschitz optimization

Yakui Huang () and Hongwei Liu
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Yakui Huang: Xidian University
Hongwei Liu: Xidian University

Computational Optimization and Applications, 2016, vol. 65, issue 3, No 6, 698 pages

Abstract: Abstract We present a smoothing projected Barzilai–Borwein (SPBB) algorithm for solving a class of minimization problems on a closed convex set, where the objective function is nonsmooth nonconvex, perhaps even non-Lipschitz. At each iteration, the SPBB algorithm applies the projected gradient strategy that alternately uses the two Barzilai–Borwein stepsizes to the smooth approximation of the original problem. Nonmonotone scheme is adopted to ensure global convergence. Under mild conditions, we prove convergence of the SPBB algorithm to a scaled stationary point of the original problem. When the objective function is locally Lipschitz continuous, we consider a general constrained optimization problem and show that any accumulation point generated by the SPBB algorithm is a stationary point associated with the smoothing function used in the algorithm. Numerical experiments on $$\ell _2$$ ℓ 2 - $$\ell _p$$ ℓ p problems, image restoration problems, and stochastic linear complementarity problems show that the SPBB algorithm is promising.

Keywords: Smoothing projected Barzilai–Borwein algorithm; Constrained non-Lipschitz optimization; Nonsmooth nonconvex optimization; Smoothing approximation; $$\ell _2$$ ℓ 2 - $$\ell _p$$ ℓ p problem; Image restoration; Stochastic linear complementarity problem (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10589-016-9854-9

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