A golden ratio primal-dual algorithm for structured convex optimization

We design, analyze and test a golden ratio primal-dual algorithm (GRPDA) for solving structured convex optimization problem, where the objective function is the sum of two closed proper convex functions, one of which involves a composition with a linear transform. GRPDA preserves all the favorable features of the classical primal-dual algorithm (PDA), i.e., the primal … Read more

Fully adaptive proximal extrapolated gradient method for monotone variational inequalities

The paper presents a fully adaptive proximal extrapolated gradient method for monotone variational inequalities. The proposed method uses fully non-monotonic and adaptive step sizes, that are computed using two previous iterates as an approximation of the locally Lipschitz constant without running a linesearch. Thus, it has almost the same low computational cost as classic proximal … Read more

A generalization of linearized alternating direction method of multipliers for solving two-block separable convex programming

The linearized alternating direction method of multipliers (ADMM), with indefinite proximal regularization, has been proved to be efficient for solving separable convex optimization subject to linear constraints. In this paper, we present a generalization of linearized ADMM (G-LADMM) to solve two-block separable convex minimization model, which linearizes all the subproblems by choosing a proper positive-definite … Read more

Optimal linearized symmetric ADMM for separable convex programming

Due to its wide applications and simple implementations, the Alternating Direction Method of Multipliers (ADMM) has been extensively investigated by researchers from different areas. In this paper, we focus on a linearized symmetric ADMM (LSADMM) for solving the multi- block separable convex minimization model. This LSADMM partitions the data into two group variables and updates … Read more

A projection algorithm based on KKT conditions for convex quadratic semidefinite programming with nonnegative constraints

The dual form of convex quadratic semidefinite programming (CQSDP) problem, with nonnegative constraints, is a 4-block separable convex optimization problem. It is known that,the directly extended 4-block alternating direction method of multipliers (ADMM4d) is very efficient to solve the dual, but its convergence is not guaranteed. In this paper, we reformulate the dual as a … Read more

Convergent Prediction-Correction-based ADMM for multi-block separable convex programming

The direct extension of the classic alternating direction method with multipliers (ADMMe) to the multi-block separable convex optimization problem is not necessarily convergent, though it often performs very well in practice. In order to preserve the numerical advantages of ADMMe and obtain convergence, many modified ADMM were proposed by correcting the output of ADMMe or … Read more