We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the relaxation of complicating constraints with gradient and fast gradient methods based on inexact first order information. Moreover, since the exact solution o...

We investigate the First-Order Primal-Dual (FPD) algorithm of Chambolle and Pock [1] in connection with MAP inference for general discrete graphical models. We provide a tight analytical upper bound of the stepsize parameter as a function of the underlying graphical structure (number of states, graph connectivity) and thus insight into the dependency of the convergence rate on the problem struc...

In this paper we present several \infeasible-start" path-following and potential-reduction primal-dual interior-point methods for nonlinear conic problems. These methods try to nd a recession direction of the feasible set of a self-dual homogeneous primal-dual problem. The methods under consideration generate an-solution for an-perturbation of an initial strictly (primal and dual) feasible prob...

In this paper, certain iterative substructuring methods with Lagrange multipliers are considered for elliptic problems in three dimensions. The algorithms belong to the family of dual{ primal FETI methods which have recently been introduced and analyzed successfully for elliptic problems in the plane. The family of algorithms for three dimensions is extended and a full analysis is provided for ...

The degree-constrained minimum spanning tree (DCMST) is relevant in the design of networks. It consists of finding a spanning tree whose nodes do not exceed a given maximum degree and whose total edge length is minimum. We design a primal branch-and-cut algorithm that solves instances of the problem to optimality. Primal methods have not been used extensively in the past, and their performance ...

In this work, we study two first-order primal-dual based algorithms, the Gradient Primal-Dual Algorithm (GPDA) and the Gradient Alternating Direction Method of Multipliers (GADMM), for solving a class of linearly constrained non-convex optimization problems. We show that with random initialization of the primal and dual variables, both algorithms are able to compute second-order stationary solu...

In this paper we present several \infeasible-start" path-following and potential-reduction primal-dual interior-point methods for nonlinear conic problems. These methods try to nd a recession direction of the feasible set of a self-dual homogeneous primal-dual problem. The methods under consideration generate an-solution for an-perturbation of an initial strictly (primal and dual) feasible prob...

The purpose of this paper is to present a new approach for solving linear programming, which has some interesting theoretical properties. In each step of the iteration, we trace a direction completely different from primal simplex method, dual simplex method, primal-dual method and interior point method. The new method is impervious to primal degeneracy and can reach a pair of exact primal and ...

In this paper, we study the local linear convergence properties of a versatile class of Primal–Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these Primal–Dual splitting methods....

In this paper, primal-dual methods for general nonconvex nonlinear optimization problems are considered. The proposed methods are exterior point type methods that permit primal variables to violate inequality constraints during the iterations. The methods are based on the exact penalty type transformation of inequality constraints and use a smooth approximation of the problem to form primal-dua...