Related papers: Iteration complexity analysis of dual first order …

We develop a novel primal-dual algorithm to solve a class of nonsmooth and nonlinear compositional convex minimization problems, which covers many existing and brand-new models as special cases. Our approach relies on a combination of a new…

We present a numerical iterative optimization algorithm for the minimization of a cost function consisting of a linear combination of three convex terms, one of which is differentiable, a second one is prox-simple and the third one is the…

Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…

Second-order methods, which utilize gradients as well as Hessians to optimize a given function, are of major importance in mathematical optimization. In this work, we prove tight bounds on the oracle complexity of such methods for smooth…

Convex quadratic programming (QP) is an important class of optimization problem with wide applications in practice. The classic QP solvers are based on either simplex or barrier method, both of which suffer from the scalability issue…

Motivated by an inertial primal-dual dynamical system with vanishing damping, we propose a class of accelerated augmented Lagrangian methods with Nesterov extrapolation parameters for a linearly constrained convex optimization problem with…

Primal-Dual Interior-Point methods are capable of solving constrained convex optimization problems to tight tolerances in a fast and robust manner. The derivatives of the primal-dual solution with respect to the problem matrices can be…

In this paper, we propose a novel primal-dual inexact gradient projection method for nonlinear optimization problems with convex-set constraint. This method only needs inexact computation of the projections onto the convex set for each…

We consider a broad class of first-order optimization algorithms which are \emph{oblivious}, in the sense that their step sizes are scheduled regardless of the function under consideration, except for limited side-information such as…

This work aims to minimize a continuously differentiable convex function with Lipschitz continuous gradient under linear equality constraints. The proposed inertial algorithm results from the discretization of the second-order primal-dual…

In this work, we revisit a classical incremental implementation of the primal-descent dual-ascent gradient method used for the solution of equality constrained optimization problems. We provide a short proof that establishes the linear…

Primal-dual methods in online optimization give several of the state-of-the art results in both of the most common models: adversarial and stochastic/random order. Here we try to provide a more unified analysis of primal-dual algorithms to…

We develop a new method for equality constrained optimization problems based on a sequential cubic programming framework. Each iteration utilizes a step decomposition based on the Jacobian of the constraints into a normal and a tangential…

A constrained optimization problem is primal infeasible if its constraints cannot be satisfied, and dual infeasible if the constraints of its dual problem cannot be satisfied. We propose a novel iterative method, named proportional-integral…

In this paper, we propose an inertial accelerated primal-dual method for the linear equality constrained convex optimization problem. When the objective function has a ``nonsmooth + smooth'' composite structure, we further propose an…

Lagrangian relaxation and approximate optimization algorithms have received much attention in the last two decades. Typically, the running time of these methods to obtain a $\epsilon$ approximate solution is proportional to…

This paper proposes and establishes the iteration-complexity of an inexact proximal accelerated augmented Lagrangian (IPAAL) method for solving linearly constrained smooth nonconvex composite optimization problems. Each IPAAL iteration…

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…

We propose a high-order version of the augmented Lagrangian method for solving convex optimization problems with linear constraints, which achieves arbitrarily fast -- and even superlinear -- convergence rates. First, we analyze the…

This note establishes a limiting formula for the conic Lagrangian dual of a convex infinite optimization problem, correcting the classical version of Karney [Math. Programming 27 (1983) 75-82] for convex semi-infinite programs. A…