The technique, called separable programming, basically replaces all separable convex functions, in objectives and constraints, by piecewise linear convex functions.

Jan 8, 2024 · In this paper, we answer this question affirmatively by developing an over-relaxed ADMM integrated with a criterion to decide whether a relaxation step is implemented in the …

We propose a splitting method for solving a separable convex minimization problem with linear constraints, where the objective function is expressed as the sum of m individual functions …

In this paper, we focus on the application of the Peaceman--Rachford splitting method (PRSM) to a convex minimization model with linear constraints and a separable objective function.

Jun 1, 2018 · In this paper, a prediction–correction-based ADMM was presented for solving a special multi-block separable convex programming, with n − 2 objective functions being linear …

We propose a novel parallel splitting ALM-based method for the separable con-vex programming problem with linear constraints, where the objective function can be expressed as the sum of …

This paper takes a fresh look at the direct application of the proximal point algorithm (PPA) to the separable convex programming with linear constraints, and proposes a customized PPA by …

Jul 4, 2017 · In this book, the author considers separable programming and, in particular, one of its important cases - convex separable programming. Some general results are presented, …

Jan 14, 2014 · We propose a splitting method for solving a separable convex minimization problem with linear constraints, where the objective function is expressed as the sum of m …

Aug 30, 2011 · The customized PPA and ADM are equally effective to exploit the separable structure of the primal problem, equally efficient in numerical senses and equally easy to …

Mar 1, 2013 · Based on ADM's straightforward extension, this paper presents a new splitting method for the model under consideration, which is empirically competitive to the …

Nov 18, 2012 · Based on ADM’s straightforward extension, this paper presents a new splitting method for the model under consideration, which is empirically competitive to the …

Dec 1, 2021 · This paper presents a novel parallel splitting method for the multiple-block separable convex optimization problem with linear equality constraints, which enjoys a larger …

Beyond computation, the duality theory in convex optimization also provides valuable analytical insights and new proofs of classical results in control. In this work, we extend this analytical …

Mar 28, 2014 · When the alternating direction method of multipliers (ADMM) is extended directly to a multi-block separable convex minimization model whose objective function is in form of …

3 days ago · In this work, we introduce a unified computational framework for a class of widely utilized quantum resource measures, derived from convex roof extensions.

As it was pointed out in Chapter Two, if f j (x j ) are strictly convex and g ij (x j ) are convex for i = 1,..., m and j ∉ L, the standard simplex method, discarding the restricted basis entry rule, is …