Ha 7] recently introduced the generalized proximal point algorithm for solving the generalized equation. In this note, we present the generalized proximal point algorithm for convex optimization problems based on Ha's work. The idea behind this algorithm is that instead of adding a quadratic term to all the variables, we add a quadratic term to a subset of the variables. We extend the criteria ...

A new algorithm, the dual active set algorithm, is presented for solving a minimization problem with equality constraints and bounds on the variables. The algorithm identifies the active bound constraints by maximizing an unconstrained dual function in a finite number of iterations. Convergence of the method is established, and it is applied to convex quadratic programming. In its implementable...

The restoration problem for Poissonian images, arising in medical and astronomical applications, is an active research area. The associated optimization models are quite challenging since the fidelity term of the problem is not a quadratic function and the regularizer is usually nonsmooth. Recently, the augmented Lagrangian-based alternating direction method has been proposed to solve the total...

This article is devoted to the numerical solution of large-scale quadratic eigenvalue problems. Such problems arise in a wide variety of applications, such as the dynamic analysis of structural mechanical systems, acoustic systems, fluid mechanics, and signal processing. We first introduce a generalized second-order Krylov subspace based on a pair of square matrices and two initial vectors and ...

In this paper, we consider a prototypical convex optimization problem with multi-block variables and separable structures. By adding the Logarithmic Quadratic Proximal (LQP) regularizer suitable proximal parameter to each of first grouped subproblems, develop partial LQP-based Alternating Direction Method Multipliers (ADMM-LQP). The dual variable is updated twice relatively larger stepsizes tha...

We devise a new generalized univariate Newton method for solving nonlinear equations, motivated by Bregman distances and proximal regularization of optimization problems. We prove quadratic convergence of the new method, a special instance of which is the classical Newton’s method. We illustrate the possible benefits of the new method over classical Newton’s method by means of test problems inv...