Regularized minimization problems with nonconvex, nonsmooth, even non-Lipschitz penalty functions have attracted much attention in recent years, owing to their wide applications in statistics, control,system identific...
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Regularized minimization problems with nonconvex, nonsmooth, even non-Lipschitz penalty functions have attracted much attention in recent years, owing to their wide applications in statistics, control,system identification and machine learning. In this paper, the non-Lipschitz ?_p(0 < p < 1) regularized matrix minimization problem is studied. A global necessary optimality condition for this non-Lipschitz optimization problem is firstly obtained, specifically, the global optimal solutions for the problem are fixedpoints of the so-called p-thresholding operator which is matrix-valued and set-valued. Then a fixedpoint iterative scheme for the non-Lipschitz model is proposed, and the convergence analysis is also addressed in detail. Moreover,some acceleration techniques are adopted to improve the performance of this algorithm. The effectiveness of the proposed p-thresholding fixedpointcontinuation(p-FPC) algorithm is demonstrated by numerical experiments on randomly generated and real matrix completion problems.
fixedpointcontinuation(FPC) algorithm is a developed version of convex optimization algorithm,which is an important research method for reconstruction of Compressed Sensing(CS).In this paper,a fast FPC(FFPC) algorit...
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fixedpointcontinuation(FPC) algorithm is a developed version of convex optimization algorithm,which is an important research method for reconstruction of Compressed Sensing(CS).In this paper,a fast FPC(FFPC) algorithm is proposed to accelerate the convergence speed of FPC *** is introduced into an efficient shifting step,and its current iteration is updated by using special linear combination of two previous *** the accuracy of each iteration is improved,and the convergence speed is *** the numerical experiments,the convergence of FFPC algorithm is proven,the convergence speed of FFPC algorithm is obviously improved compared with the standard FPC algorithm,and the reconstruction quality is better than other algorithms.
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