Related papers: A heavy-ball type curve search method for smooth c…
Heavy Ball (HB) nowadays is one of the most popular momentum methods in non-convex optimization. It has been widely observed that incorporating the Heavy Ball dynamic in gradient-based methods accelerates the training process of modern…
Lower-bound analyses for nonconvex strongly-concave minimax optimization problems have shown that stochastic first-order algorithms require at least $\mathcal{O}(\varepsilon^{-4})$ oracle complexity to find an $\varepsilon$-stationary…
A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…
When considering the minimization of a quadratic or strongly convex function, it is well known that first-order methods involving an inertial term weighted by a constant-in-time parameter are particularly efficient (see Polyak [32],…
Projected-search methods for bound-constrained optimization are based on performing a search along a piecewise-linear continuous path obtained by projecting a search direction onto the feasible region. A benefit of these methods is that…
Two algorithms are proposed, analyzed, and tested for solving continuous optimization problems with nonlinear equality constraints. Each is an extension of a stochastic momentum-based method from the unconstrained setting to the setting of…
In this paper, we consider the problem of minimizing a difference-of-convex objective over a nonlinear conic constraint, where the cone is closed, convex, pointed and has a nonempty interior. We assume that the support function of a compact…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
Optimization models with non-convex constraints arise in many tasks in machine learning, e.g., learning with fairness constraints or Neyman-Pearson classification with non-convex loss. Although many efficient methods have been developed…
We further research on the accelerated optimization phenomenon on Riemannian manifolds by introducing accelerated global first-order methods for the optimization of $L$-smooth and geodesically convex (g-convex) or $\mu$-strongly g-convex…
This work focuses on convergence analysis of the projected gradient method for solving constrained convex minimization problem in Hilbert spaces. We show that the sequence of points generated by the method employing the Armijo linesearch…
In this work, a nonlinear momentum method is introduced to enhance the convergence performance of momentum-based gradient optimization algorithms. Classical momentum methods, such as the Heavy Ball method, can be viewed as a dynamical…
In this work, we analyze the convergence of Polyak's heavy ball method in both continuous and discrete time for non-convex $C^4$-objective functions satisfying the Polyak-Lojasiewicz inequality. Under this weak assumption, we recover the…
In this paper, acceleration of gradient methods for convex optimization problems with weak levels of convexity and smoothness is considered. Starting from the universal fast gradient method which was designed to be an optimal method for…
We derive lower bounds on the black-box oracle complexity of large-scale smooth convex minimization problems, with emphasis on minimizing smooth (with Holder continuous, with a given exponent and constant, gradient) convex functions over…
Stochastic gradient descent with momentum (SGDM) methods have become fundamental optimization tools in machine learning, combining the computational efficiency of stochastic gradients with the acceleration benefits of momentum. Despite…
This paper considers the fixed point problem for a nonexpansive mapping on a real Hilbert space and proposes novel line search fixed point algorithms to accelerate the search. The termination conditions for the line search are based on the…
We develop a distributed algorithm for convex Empirical Risk Minimization, the problem of minimizing large but finite sum of convex functions over networks. The proposed algorithm is derived from directly discretizing the second-order…
We aim at computing the derivative of the solution to a parametric optimization problem with respect to the involved parameters. For a class broader than that of strongly convex functions, this can be achieved by automatic differentiation…
This paper primarily focuses on computing the Euclidean projection of a vector onto the $\ell_{p}$ ball in which $p\in(0,1)$. Such a problem emerges as the core building block in statistical machine learning and signal processing tasks…