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In this paper, we develop an inexact Bregman proximal gradient (iBPG) method based on a novel two-point inexact stopping condition, and establish the iteration complexity of $mathcal{O}(1/k)$ as well as the convergence of the sequence under some proper conditions. To improve the convergence speed, we further develop an inertial variant of our iBPG (denoted by v-iBPG) and show that it has the iteration complexity of $mathcal{O}(1/k^{gamma})$, where $gammageq1$ is a restricted relative smoothness exponent. Thus, when $gamma>1$, the v-iBPG readily improves the $mathcal{O}(1/k)$ convergence rate of the iBPG. In addition, for the case of using the squared Euclidean distance as the kernel function, we further develop a new inexact accelerated proximal gradient (iAPG) method, which can circumvent the underlying feasibility difficulty often appearing in existing inexact conditions and inherit all desirable convergence properties of the exact APG under proper summable-error conditions. Finally, we conduct some preliminary numerical experiments for solving a relaxation of the quadratic assignment problem to demonstrate the convergence behaviors of the iBPG, v-iBPG and iAPG under different inexactness settings.
We study a general convex optimization problem, which covers various classic problems in different areas and particularly includes many optimal transport related problems arising in recent years. To solve this problem, we revisit the classic Bregman
In this paper, we consider an accelerated method for solving nonconvex and nonsmooth minimization problems. We propose a Bregman Proximal Gradient algorithm with extrapolation(BPGe). This algorithm extends and accelerates the Bregman Proximal Gradien
We propose a novel algorithmic framework of Variable Metric Over-Relaxed Hybrid Proximal Extra-gradient (VMOR-HPE) method with a global convergence guarantee for the maximal monotone operator inclusion problem. Its iteration complexities and local li
In this paper, we compute the stationary states of the multicomponent phase-field crystal model by formulating it as a block constrained minimization problem. The original infinite-dimensional non-convex minimization problem is approximated by a fini
Sparsity-inducing regularization problems are ubiquitous in machine learning applications, ranging from feature selection to model compression. In this paper, we present a novel stochastic method -- Orthant Based Proximal Stochastic Gradient Method (