This paper takes a uniform look at the customized applications of proximal point algorithm (PPA) to two classes of problems: the linearly constrained convex minimization problem with a generic or separable objective function and a saddle-point problem. We model these two classes of problems uniformly by a mixed variational inequality, and show how PPA with … Read more
Recently, we have proposed to combine the alternating direction method (ADM) with a Gaussian back substitution procedure for solving the convex minimization model with linear constraints and a general separable objective function, i.e., the objective function is the sum of many functions without coupled variables. In this paper, we further study this topic and show … Read more
We consider a general class of convex optimization problems in which one seeks to minimize a strongly convex function over a closed and convex set which is by itself an optimal set of another convex problem. We introduce a gradient-based method, called the minimal norm gradient method, for solving this class of problems, and establish … Read more
The perceptron algorithm, introduced in the late fifties in the machine learning community, is a simple greedy algorithm for finding a solution to a finite set of linear inequalities. The algorithm’s main advantages are its simplicity and noise tolerance. The algorithm’s main disadvantage is its slow convergence rate. We propose a modified version of the … Read more
In this work we consider the symmetric network equilibrium problem formulated as convex minimization problem whose variables are the path flows. In order to take into account the difficulties related to the large dimension of real network problems we adopt a column generation strategy and we employ a gradient projection method within an inexact decomposition … Read more
We consider multi-target linear-quadratic control problem on semi-infinite interval. We show that the problem can be reduced to a simple convex optimization problem on the simplex. CitationTo appear in Mathematical Problems in Engineering 2012 ArticleDownload View PDF
Orthogonal frequency division multiplexing (OFDM) is a technique that will prevail in the next generation wireless communication. Channel estimation is one of the key challenges in OFDM, since high-resolution channel estimation can significantly improve the equalization at the receiver and consequently enhance the communication performances. In this paper, we propose a system with an asymmetric … Read more
The old alternating direction method (ADM) has found many new applications recently, and its empirical efficiency has been well illustrated in various fields. However, the estimate of ADM’s convergence rate remains a theoretical challenge for a few decades. In this note, we provide a uniform proof to show the O(1/t) convergence rate for both the … Read more
The accelerated proximal gradient (APG) method, first proposed by Nesterov, and later refined by Beck and Teboulle, and studied in a unifying manner by Tseng has proven to be highly efficient in solving some classes of large scale structured convex optimization (possibly nonsmooth) problems, including nuclear norm minimization problems in matrix completion and $l_1$ minimization … Read more
We introduce and study the Split Common Null Point Problem (SCNPP) for set-valued maximal monotone mappings in Hilbert space. This problem generalizes our Split Variational Inequality Problem (SVIP) [Y. Censor, A. Gibali and S. Reich, Algorithms for the split variational inequality problem, Numerical Algorithms, accepted for publication, DOI 10.1007/s11075-011-9490-5]. The SCNPP with only two set-valued … Read more