This article discusses nonconforming finite element methods for convex minimization problems and systematically derives dual mixed formulations. Duality relations lead to simple error estimates that avoid an explicit treatment of nonconformity errors. A reconstruction formula provides the discrete solution problem via a postprocessing procedure which implies strong duality relation is interest ...

Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for solving optimization problems. In this paper, we present a new framework for establishing error bounds for a class of structured convex optimization problems, in ...

In this paper, we propose a new iterative scheme with the help of gradient- projection algorithm (GPA) for finding common solution an equilibrium problem, constrained convex minimization and fixed point problem. Then, prove some strong convergence theorems which improve extend recent results. Moreover, give numerical result to show validity our main theorem.

Given a set of polyhedral cones C1, · · · , Ck ⊂ R, and a convex set D, does the union of these cones cover the set D? In this paper we consider the computational complexity of this problem for various cases such as whether the cones are defined by extreme rays or facets, and whether D is the entire R or a given linear subspace R. As a consequence, we show that it is coNP-complete to decide if ...

Regularized risk minimization often involves nonsmooth optimization. This can be particularly challenging when the regularizer is a sum of simpler regularizers, as in the overlapping group lasso. Very recently, this is alleviated by using the proximal average, in which an implicitly nonsmooth function is employed to approximate the composite regularizer. In this paper, we propose a novel extens...

The affine rank minimization problem, which consists of finding a matrix of minimum rank subject to linear equality constraints, has been proposed in many areas of engineering and science. A specific rank minimization problem is the matrix completion problem, in which we wish to recover a (low-rank) data matrix from incomplete samples of its entries. A recent convex relaxation of the rank minim...

Algorithms for projecting a point onto the intersection of convex sets are useful subroutines for solving optimization problems with constraints. One such algorithm is the Dykstra's algorithm, which is known to be alternating minimization on the dual problem. The projection onto each convex set generates a halfspace supporting the set. It is also relatively easy to project onto the intersection...

The affine rank minimization problem, which consists of finding a matrix of minimum rank subject to linear equality constraints, has been proposed in many areas of engineering and science. A specific rank minimization problem is the matrix completion problem, in which we wish to recover a (low-rank) data matrix from incomplete samples of its entries. A recent convex relaxation of the rank minim...