Alternating direction method of multipliers (ADMM) has been widely used in many applications due to its promising performance to solve complex regularization problems and large-scale distributed optimization problems. Stochastic ADMM, which visits only one sample or a mini-batch of samples each time, has recently been proved to achieve better performance than batch ADMM. However, most stochasti...

In this paper we adapt the well-known parametric approach from fractional programming to solve a class of fractional programs with a noncompact feasible region. Such fractional problems belong to an important class of single component preventive maintenance models. Moreover, for a special but important subclass we show that the subproblems occurring in this parametric approach are easy solvable...

On adaptively refined quadrilateral or hexahedral meshes, one usually employs constraints on degrees of freedom to deal with hanging nodes. How these constraints are constructed is relatively straightforward for conforming finite element methods: The constraints are used to ensure that the discrete solution space remains a subspace of the continuous space. On the other hand, for nonconforming m...

The Alternating Direction Method of Multipliers (ADMM) has been studied for years. Traditional ADMM algorithms need to compute, at each iteration, an (empirical) expected loss function on all training examples, resulting in a computational complexity proportional to the number of training examples. To reduce the complexity, stochastic ADMM algorithms were proposed to replace the expected loss f...

In this paper, we propose a new stochastic alternating direction method of multipliers (ADMM) algorithm, which incrementally approximates the full gradient in the linearized ADMM formulation. Besides having a low per-iteration complexity as existing stochastic ADMM algorithms, the proposed algorithm improves the convergence rate on convex problems from O ( 1 √ T ) to O ( 1 T ) , where T is the ...

In the context of convex optimization problems in Hilbert spaces, we induce inertial effects into the classical ADMM numerical scheme and obtain in this way so-called inertial ADMM algorithms, the convergence properties of which we investigate into detail. To this aim we make use of the inertial version of the DouglasRachford splitting method for monotone inclusion problems recently introduced ...

Jiang, H. and Y.S. Wong, A parallel alternating direction implicit preconditioning method, Journal of Computational and Applied Mathematics 36 (1991) 209-226. The alternating direction implicit (ADI) iterative method is an efficient iterative method to solve systems of linear equations due to its extremely fast convergence. The AD1 method has also been used successfully as a preconditioner in s...

We introduce a new barrier function which is not a barrier function in the usual sense: it has finite value at the boundary of the feasible region. Despite this, its iteration bound, O (√ n logn log n ε ) , is as good as it can be: it is the best known bound for large-update methods. The recently introduced notions of superconvexity and exponential convexity are crucial in the analysis.

in many infeasible linear programs it is important to construct it to a feasible problem with a minimum pa-rameters changing corresponding to a given nonnegative vector. this paper defines a new inverse problem, called “inverse feasible problem”. for a given infeasible polyhedron and an n-vector a minimum perturba-tion on the parameters can be applied and then a feasible polyhedron is concluded.

PURPOSE The three-dimensional (3D) dose distribution covering a tumor region tends to be more breakable if the beam's eye view (BEV) of the 3D electron density (ED) map in a beam direction changes more abruptly with large fluctuations. Our aim of this study was to develop an automated determination method of robust beam directions against the patient setup error based on the ED-based BEV in the...