Related papers: Accelerated first-order methods for convex optimiz…
In this paper, a new theory is developed for first-order stochastic convex optimization, showing that the global convergence rate is sufficiently quantified by a local growth rate of the objective function in a neighborhood of the optimal…
This paper introduces new parameter-free first-order methods for convex optimization problems in which the objective function exhibits H\"{o}lder smoothness. Inspired by the recently proposed distance-over-gradient (DOG) technique, we…
In this paper we provide a detailed analysis of the iteration complexity of dual first order methods for solving conic convex problems. When it is difficult to project on the primal feasible set described by convex constraints, we use the…
First-order optimization methods are crucial for solving large-scale data processing problems, particularly those involving convex non-smooth composite objectives. For such problems with convex non-smooth composite objectives, we introduce…
Consider the stochastic composition optimization problem where the objective is a composition of two expected-value functions. We propose a new stochastic first-order method, namely the accelerated stochastic compositional proximal gradient…
Motivated, in particular, by the entropy-regularized optimal transport problem, we consider convex optimization problems with linear equality constraints, where the dual objective has Lipschitz $p$-th order derivatives, and develop two…
Two accelerated first-order methods, HNAG$^+$ and HNAG$^{++}$, are presented for smooth strongly convex optimization. By optimizing the coercivity constant of the HNAG flow and using a refined Lyapunov analysis, it is shown that HNAG$^+$…
This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…
Nonlinearly constrained nonconvex and nonsmooth optimization models play an increasingly important role in machine learning, statistics and data analytics. In this paper, based on the augmented Lagrangian function we introduce a flexible…
In this paper we consider stochastic composite convex optimization problems with the objective function satisfying a stochastic bounded gradient condition, with or without a quadratic functional growth property. These models include the…
We propose computationally tractable accelerated first-order methods for Riemannian optimization, extending the Nesterov accelerated gradient (NAG) method. For both geodesically convex and geodesically strongly convex objective functions,…
We introduce a new form of Lagrangian and propose a simple first-order algorithm for nonconvex optimization with nonlinear equality constraints. We show the algorithm generates bounded dual iterates, and establish the convergence to KKT…
Generating motions for robots interacting with objects of various shapes is a complex challenge, further complicated by the robot geometry and multiple desired behaviors. While current robot programming tools (such as inverse kinematics,…
With the advancement of modern applications, an increasing number of composite optimization problems arise whose smooth component does not possess a globally Lipschitz continuous gradient. This setting prevents the direct use of the…
This paper develops and analyzes an accelerated proximal descent method for finding stationary points of nonconvex composite optimization problems. The objective function is of the form $f+h$ where $h$ is a proper closed convex function,…
The linear primal-dual hybrid gradient (PDHG) method is a first-order method that splits convex optimization problems with saddle-point structure into smaller subproblems. Unlike those obtained in most splitting methods, these subproblems…
This paper introduces a first-order method for solving optimal powered descent guidance (PDG) problems, that directly handles the nonconvex constraints associated with the maximum and minimum thrust bounds with varying mass and the pointing…
Conditional gradients constitute a class of projection-free first-order algorithms for smooth convex optimization. As such, they are frequently used in solving smooth convex optimization problems over polytopes, for which the computational…
We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [5] by taking a different…
In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. We justify local superlinear convergence under the assumption of uniform convexity of the smooth…