A novel proximal difference-of-convex (DC) algorithmic framework to solve general non-convex, non-smooth optimization problems is proposed by combining Barzilai-Borwein (BB) step sizes with nonmonotone line search strategies and develops extrapolation mechanisms to accelerate convergence while ensuring global stability.
Abstract
The paper proposes a novel proximal difference-of-convex (DC) algorithmic framework to solve general non-convex, non-smooth optimization problems. By combining Barzilai-Borwein (BB) step sizes with nonmonotone line search strategies, our approach effectively overcomes the conservative step sizes and stability issues inherent in standard proximal DC algorithms. Furthermore, we develop extrapolation mechanisms to accelerate convergence while ensuring global stability. The global convergence of the proposed algorithms is rigorously established under the Kurdyka-\L ojasiewicz property. Numerical experiments on the SCAD-regularized least squares problem and graphic Ginzburg-Landau image segmentation models demonstrate that the proposed methods achieve highly competitive efficiency and accuracy compared to existing DC algorithms.
The proposed AdaBBNC incorporates a flexible BB-based curvature estimate into the proximal gradient framework to enhance adaptability in nonconvex settings and achieves the optimal iteration complexity of $\mathcal{O}(\epsilon^{-2})$ for finding an $\epsilon$-stationary point, without requiring any prior knowledge of t...
In this paper, we propose a proximal gradient method with adaptive linesearch for multiobjective optimization problems whose objective functions are weakly smooth, i.e., they have H\"older continuous gradients. The proposed method is parameter-free as we do not require prior knowledge of parameters related to the weak...
The Barzilai and Borwein methods are renowned for their simplicity and numerical efficiency, attracting significant attention for large-scale optimization problems. Recently, a new adaptive Barzilai and Borwein method with a nonmonotone line search has been proposed for general unconstrained optimization. Building on t...
A. Ibrahim, F. Mofarreh· Discover Computing· 0 citations
The results show that the proposed Wolfe-type spectral conjugate gradient method performs competitively overall, matching or outperforming existing methods on most problems tested, while a few specific limitations of the current implementation are also identified and discussed.
The stochastic recursive gradient algorithm (SARAH) has garnered considerable attention owing to its implementation of a straightforward recursive framework for stochastic gradient updates. Motivated by this, we propose to integrate the importance sampling strategy with mini-batch techniques into the SARAH framework, d...
Lei Liu, Hai-Lin Sun, Dan Xue· Asia-Pacific Journal of Oper...· 0 citations
As an extension of convex quadratic optimization (CQO) problems, the weighted convex quadratic optimization (WCQO) plays an important role in the domain of mathematical programming and engineering. In this paper, we propose a short-step primal-dual interior-point algorithm for solving WCQO based on the strategy of weig...
Rima Hamadouche, L. Derbal, M. Achache· Reserche operationelle· 0 citations
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