Novel DCA based algorithms for a special class of nonconvex problems with application in machine learning

Hoai An Le Thi, Hoai Minh Le, Duy Nhat Phan and Bach Tran

Applied Mathematics and Computation, 2021, vol. 409, issue C

Abstract: We address the problem of minimizing the sum of a nonconvex, differentiable function and composite functions by DC (Difference of Convex functions) programming and DCA (DC Algorithm), powerful tools of nonconvex optimization. The main idea of DCA relies on DC decompositions of the objective function, it consists in approximating a DC (nonconvex) program by a sequence of convex ones. We first develop a standard DCA scheme especially dealing with the very specific structure of this problem. Furthermore, we extend DCA to give rise to the so-named DCA-Like, which is based on a new and efficient way to approximate the DC objective function without knowing a DC decomposition. We further improve DCA based algorithms by incorporating the Nesterov’s acceleration technique into them. The convergence properties and the convergence rate under Kurdyka-Łojasiewicz assumption of extended DCAs are rigorously studied. We prove that DCA-Like and the accelerated versions subsequently converge from every initial point to a critical point of the considered problem. Finally, we investigate the proposed algorithms for an important problem in machine learning: the t-distributed stochastic neighbor embedding. Numerical experiments on several benchmark datasets illustrate the efficiency of our algorithms.

Keywords: DC programming; DCA; DCA-Like; Accelerated DCA; Accelerated DCA-Like; Sum of nonconvex function and composite functions; Dimensionality reduction; t-distributed Stochastic Neighbor Embedding (t-SNE) (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300320308572

DOI: 10.1016/j.amc.2020.125904

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