Related papers: A generic coordinate descent solver for nonsmooth …
We propose a descent subgradient algorithm for unconstrained nonsmooth nonconvex multiobjective optimization problems. To find a descent direction, we present an iterative process that efficiently approximates the Goldstein subdifferential…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
We present a novel, practical, and provable approach for solving diagonally constrained semi-definite programming (SDP) problems at scale using accelerated non-convex programming. Our algorithm non-trivially combines acceleration motions…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
In this paper, we analyze the mirror descent algorithm for non-smooth optimization problems in which the objective function is relatively strongly convex, without relying on the standard Lipschitz continuity assumption commonly used in the…
For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…
Coordinate descent methods employ random partial updates of decision variables in order to solve huge-scale convex optimization problems. In this work, we introduce new adaptive rules for the random selection of their updates. By adaptive,…
We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…
This paper proposes a new steepest gradient descent method for solving nonconvex finite minimax problems using non-monotone adaptive step sizes and providing proof of convergence results in cases of the nonconvex, quasiconvex, and…
This paper proposes a homogeneous second-order descent framework (HSODF) for nonconvex and convex optimization based on the generalized homogeneous model (GHM). In comparison to the Newton steps, the GHM can be solved by extremal symmetric…
We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…
Least Absolute Deviations (LAD) regression provides a robust alternative to ordinary least squares by minimizing the sum of absolute residuals. However, its widespread use has been limited by the computational cost of existing solvers,…
In this paper we present a nonmonotone line search subgradient algorithm tailored to upper-$\mathcal{C}^2$ functions. This is a family of nonsmooth and nonconvex functions that satisfies a nonsmooth and local version of the descent lemma,…
We develop a new consensus-based distributed algorithm for solving learning problems with feature partitioning and non-smooth convex objective functions. Such learning problems are not separable, i.e., the associated objective functions…
Continuous optimization is an important problem in many areas of AI, including vision, robotics, probabilistic inference, and machine learning. Unfortunately, most real-world optimization problems are nonconvex, causing standard convex…
There is a recent surge of interest in nonconvex reformulations via low-rank factorization for stochastic convex semidefinite optimization problem in the purpose of efficiency and scalability. Compared with the original convex formulations,…
Convex separable quadratic optimization problems occur in many practical applications. In this paper, based on an iterative resolution scheme of the KKT system, we develop an efficient method for solving a quadratic programming problem with…
In this work, we analyze the global convergence property of coordinate gradient descent with random choice of coordinates and stepsizes for non-convex optimization problems. Under generic assumptions, we prove that the algorithm iterate…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…
In this paper, a modification to the Gradient Sampling (GS) method for minimizing nonsmooth nonconvex functions is presented. One drawback in GS method is the need of solving a Quadratic optimization Problem (QP) at each iteration, which is…