Related papers: A Variable Metric and Nesterov Extrapolated Proxim…
This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…
This paper introduces a coordinate descent version of the V\~u-Condat algorithm. By coordinate descent, we mean that only a subset of the coordinates of the primal and dual iterates is updated at each iteration, the other coordinates being…
In this paper, we aim at solving the cardinality constrained high-order portfolio optimization, i.e., mean-variance-skewness-kurtosis model with cardinality constraint (MVSKC). Optimization for the MVSKC model is of great difficulty in two…
This paper has two primary objectives. First, we investigate fundamental qualitative properties of the generalized multi-source Weber problem formulated using the Minkowski gauge function. This includes proving the existence of global…
We develop a projected Nesterov's proximal-gradient (PNPG) approach for sparse signal reconstruction that combines adaptive step size with Nesterov's momentum acceleration. The objective function that we wish to minimize is the sum of a…
This paper presents a simple primal dual method named DPD which is a flexible framework for a class of saddle point problem with or without strongly convex component. The presented method has linearized version named LDPD and exact version…
In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…
Accurate signal recovery or image reconstruction from indirect and possibly undersampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by…
A new decomposition optimization algorithm, called \textit{path-following gradient-based decomposition}, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this…
We consider stochastic optimization of a smooth non-convex loss function with a convex non-smooth regularizer. In the online setting, where a single sample of the stochastic gradient of the loss is available at every iteration, the problem…
The paper studies decentralized optimization over networks, where agents minimize a composite objective consisting of the sum of smooth convex functions--the agents' losses--and an additional nonsmooth convex extended value function. We…
For the composite multi-objective optimization problem composed of two nonsmooth terms, a smoothing method is used to overcome the nonsmoothness of the objective function, making the objective function contain at most one nonsmooth term.…
Submodular functions, defined on continuous or discrete domains, arise in numerous applications. We study the minimization of the difference of two submodular (DS) functions, over both domains, extending prior work restricted to set…
We propose a proximal variable smoothing algorithm for nonsmooth optimization problem with sum of three functions involving weakly convex composite function. The proposed algorithm is designed as a time-varying forward-backward splitting…
The paper studies decentralized optimization over networks, where agents minimize a sum of {\it locally} smooth (strongly) convex losses and plus a nonsmooth convex extended value term. We propose decentralized methods wherein agents {\it…
Sentence compression is an important problem in natural language processing with wide applications in text summarization, search engine and human-AI interaction system etc. In this paper, we design a hybrid extractive sentence compression…
We propose a new stochastic coordinate descent method for minimizing the sum of convex functions each of which depends on a small number of coordinates only. Our method (APPROX) is simultaneously Accelerated, Parallel and PROXimal; this is…
The Mean-Variance-Skewness-Kurtosis (MVSK) portfolio optimization model is a quartic nonconvex polynomial minimization problem over a polytope, which can be formulated as a Difference-of-Convex (DC) program. In this manuscript, we…
The stable principal component pursuit (SPCP) is a non-smooth convex optimization problem, the solution of which enables one to reliably recover the low rank and sparse components of a data matrix which is corrupted by a dense noise matrix,…
The nonlinear conjugate gradient methods are known to be an effective approach for standard unconstrained optimization problems especially for large-scale problems. This paper proposes a proximal nonlinear conjugate gradient method, which…