Related papers: Parameter-free proximal bundle methods with adapti…

We consider solving nonconvex composite optimization problems in which the sum of a smooth function and a nonsmooth function is minimized. Many of convergence analyses of proximal gradient-type methods rely on global descent property…

In this paper, we propose new proximal Newton-type methods for convex optimization problems in composite form. The applications include model predictive control (MPC) and embedded MPC. Our new methods are computationally attractive since…

Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the…

In this paper, we combine the positive aspects of the Gradient Sampling (GS) and bundle methods, as the most efficient methods in nonsmooth optimization, to develop a robust method for solving unconstrained nonsmooth convex optimization…

Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…

We propose a new bundle-based augmented Lagrangian framework for solving constrained convex problems. Unlike the classical (inexact) augmented Lagrangian method (ALM) that has a nested double-loop structure, our framework features a…

Adaptive atomistic/continuum (a/c) coupling method is an important method for the simulation of material and atomistic systems with defects to achieve the balance of accuracy and efficiency. Residual based a posteriori error estimator is…

We suggest simple modifications of the conditional gradient method for smooth optimization problems, which maintain the basic convergence properties, but reduce the implementation cost of each iteration essentially. Namely, we propose the…

Gradient descent is slow to converge for ill-conditioned problems and non-convex problems. An important technique for acceleration is step-size adaptation. The first part of this paper contains a detailed review of step-size adaptation…

Using convex combination and linesearch techniques, we introduce a novel primal-dual algorithm for solving structured convex-concave saddle point problems with a generic smooth nonbilinear coupling term. Our adaptive linesearch strategy…

We study the problem of parameter-free stochastic optimization, inquiring whether, and under what conditions, do fully parameter-free methods exist: these are methods that achieve convergence rates competitive with optimally tuned methods,…

Alternating direction multiplication is a powerful technique for solving convex optimisation problems. When challenging subproblems are encountered in the real world, it is useful to solve them by introducing neighbourhood terms. When the…

For solving a broad class of nonconvex programming problems on an unbounded constraint set, we provide a self-adaptive step-size strategy that does not include line-search techniques and establishes the convergence of a generic approach…

In this paper, we propose a unified two-phase scheme to accelerate any high-order regularized tensor approximation approach on the smooth part of a composite convex optimization model. The proposed scheme has the advantage of not needing to…

We investigate the proximal point algorithm (PPA) and its inexact extensions under an error bound condition, which guarantees a global linear convergence if the proximal regularization parameter is larger than the error bound condition…

Selecting an effective step-size is a fundamental challenge in first-order optimization, especially for problems with non-Euclidean geometries. This paper presents a novel adaptive step-size strategy for optimization algorithms that rely on…

In this paper, we consider a nonsmooth convex finite-sum problem with a conic constraint. To overcome the challenge of projecting onto the constraint set and computing the full (sub)gradient, we introduce a primal-dual incremental gradient…

We study the worst-case convergence rates of the proximal gradient method for minimizing the sum of a smooth strongly convex function and a non-smooth convex function whose proximal operator is available. We establish the exact worst-case…

Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…

In this work, we solve a 49-year open problem, the general optimal step-size for ADMM-type algorithms. For a convex program: $\text{min.} \,\, f({x}) + g({z})$, $\text{s.t.}\, {A}{x} - {B}{z} = {c} $, given an arbitrary fixed-point…