In this paper, we extend the improved pointwise iteration-complexity result of a dynamic regularized alternating direction method of multipliers (ADMM) for a new stepsize domain. In this complexity analysis, the stepsize parameter can even be chosen in the interval $(0,2)$ instead of interval $(0,(1+\sqrt{5})/2)$. As usual, our analysis is established by interpreting this ADMM variant … Read more
In this study, we consider the special case of the uncapacitated p-hub center problem, where the weight/flow matrix includes 0 entities. In some real life networks, such as airline networks, cargo networks etc., the zero flow might exist between certain demand points. Typically in airline networks, nobody travels from city i to city i. In … Read more
Due to update the Lagrangian multiplier twice at each iteration, the symmetric alternating direction method of multipliers (S-ADMM) often performs better than other ADMM-type methods. In practice, some proximal terms with positive definite proximal matrices are often added to its subproblems, and it is commonly known that large proximal parameter of the proximal term often … Read more
This paper introduces a derivative-free and ready-to-use solver for nonlinear programs with nonlinear equality and inequality constraints (NLPs). Using finite differences and a sequential quadratic programming (SQP) approach, the algorithm aims at finding a local minimizer and no extra attempt is made to generate a globally optimal solution. Due to the use of finite differences, … Read more
We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. More’ and G. Toraldo, SIAM J. Optim. 1, 1991], our approach alternates between two phases until convergence: an identification phase, which performs gradient projection iterations … Read more
In this article, we provide an overview of the current state of the art with respect to solution of mixed integer linear optimization problems (MILPS) in parallel. Sequential algorithms for solving MILPs have improved substantially in the last two decades and commercial MILP solvers are now considered effective off-the-shelf tools for optimization. Although concerted development … Read more
We propose in this paper a unifying scheme for several algorithms from the literature dedicated to the solving of monotone inclusion problems involving compositions with linear continuous operators in infinite dimensional Hilbert spaces. We show that a number of primal-dual algorithms for monotone inclusions and also the classical ADMM numerical scheme for convex optimization problems, … Read more
In this paper, we study the local linear convergence properties of a versatile class of Primal–Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these Primal–Dual splitting methods. … Read more
In this paper, we consider symmetric binary programs that contain set packing, partitioning, or covering inequalities. To handle symmetries as well as set packing, partitioning, or covering constraints simultaneously, we introduce constrained symresacks which are the convex hull of all binary points that are lexicographically not smaller than their image w.r.t. a coordinate permutation and … Read more
A regular timetable is a collection of events that repeat themselves every specific time span. This even structure, whenever applied at a whole network, leads to several benefits both for users and the company, although some issues are introduced, especially about dimensioning the service. It is therefore fundamental to properly consider the interaction between the … Read more