Related papers: Approaching nonsmooth nonconvex optimization probl…
Convergence analysis of accelerated first-order methods for convex optimization problems are presented from the point of view of ordinary differential equation solvers. A new dynamical system, called Nesterov accelerated gradient flow, has…
In machine learning research, the proximal gradient methods are popular for solving various optimization problems with non-smooth regularization. Inexact proximal gradient methods are extremely important when exactly solving the proximal…
In this paper, we propose a second-order continuous primal-dual dynamical system with time-dependent positive damping terms for a separable convex optimization problem with linear equality constraints. By the Lyapunov function approach, we…
Many large-scale and distributed optimization problems can be brought into a composite form in which the objective function is given by the sum of a smooth term and a nonsmooth regularizer. Such problems can be solved via a proximal…
We present new convolution based smooth approximations to the absolute value function and apply them to construct gradient based algorithms such as the nonlinear conjugate gradient scheme to obtain sparse, regularized solutions of linear…
In this paper, we design and analyze a new family of adaptive subgradient methods for solving an important class of weakly convex (possibly nonsmooth) stochastic optimization problems. Adaptive methods that use exponential moving averages…
We investigate an inertial algorithm of gradient type in connection with the minimization of a nonconvex differentiable function. The algorithm is formulated in the spirit of Nesterov's accelerated convex gradient method. We prove some…
In this paper, we consider a multi-block generalized alternating direction method of multiplier (GADMM) algorithm for minimizing a linearly constrained separable nonconvex and possibly nonsmooth optimization problem. The GADMM generalizes…
In a Hilbert setting we aim to study a second order in time differential equation, combining viscous and Hessian-driven damping, containing a time scaling parameter function and a Tikhonov regularization term. The dynamical system is…
In this article a family of second order ODEs associated to inertial gradient descend is studied. These ODEs are widely used to build trajectories converging to a minimizer $x^*$ of a function $F$, possibly convex. This family includes the…
We propose and analyze a randomized zeroth-order approach based on approximating the exact gradient byfinite differences computed in a set of orthogonal random directions that changes with each iteration. A number ofpreviously proposed…
This paper proposes a projection-free primal-dual dynamics for the nonsmooth composite optimization problems with equality and inequality constraints. To deal with optimization constraints, this paper departs from the use of gradient…
We consider in this paper a class of single-ratio fractional minimization problems, in which the numerator part of the objective is the sum of a nonsmooth nonconvex function and a smooth nonconvex function while the denominator part is a…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth…
We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…
We propose a primal-dual smoothing framework for finding a near-stationary point of a class of non-smooth non-convex optimization problems with max-structure. We analyze the primal and dual gradient complexities of the framework via two…
We analyze stochastic gradient algorithms for optimizing nonconvex, nonsmooth finite-sum problems. In particular, the objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a possibly…
We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions…
We propose an unconstrained optimization method based on the well-known primal-dual hybrid gradient (PDHG) algorithm. We first formulate the optimality condition of the unconstrained optimization problem as a saddle point problem. We then…