Cluster analysis refers to finding subsets of vertices of a graph (called clusters) which are more likely to be joined pairwise than vertices in different clusters. In the last years this topic has been studied by many researchers, and several methods have been proposed. One of the most popular is to maximize the modularity, which … Read more
This paper describes three recent tools for dealing with primal degeneracy in linear programming. The first one is the Improved Primal Simplex (IPS) algorithm which turns degeneracy into a possible advantage. The constraints of the original problem are dynamically partitioned based on the numerical values of the current basic variables. The idea is to work … Read more
It is well known that any feasible arc-flow solution to a network problem defined on a graph $G = (N, A)$, where $N$ is the set of nodes whereas $A$ is the set of arcs, can be expressed using at most $|A| + |N|$ paths and cycles having nonzero flow, out of these, at most … Read more
We present an iterative primal-dual solver for nonconvex equality-constrained quadratic optimization subproblems. The solver constructs the primal and dual trial steps from the subspace generated by the generalized Arnoldi procedure used in flexible GMRES (FGMRES). This permits the use of a wide range of preconditioners for the primal-dual system. In contrast with FGMRES, the proposed … Read more
Constraints matrices with block-angular structures are pervasive in Optimization. Interior-point methods have shown to be competitive for these structured problems by exploiting the linear algebra. One of these approaches solved the normal equations using sparse Cholesky factorizations for the block constraints, and a preconditioned conjugate gradient (PCG) for the linking constraints. The preconditioner is based … Read more
In this paper, we investigate a parallel subspace correction framework for composite convex optimization. The variables are first divided into a few blocks based on certain rules. At each iteration, the algorithms solve a suitable subproblem on each block simultaneously, construct a search direction by combining their solutions on all blocks, then identify a new … Read more
We contribute to the theory for minimal liftings of cut-generating functions. In particular, we give three operations that preserve the so-called covering property of certain structured cut-generating functions. This has the consequence of vastly expanding the set of undominated cut generating functions which can be used computationally, compared to known examples from the literature. The … Read more
Gas network optimization manages the gas transport by minimizing operating costs and fulfilling contracts between consumers and suppliers. This is an NP- hard problem governed by non-convex and nonlinear gas transport functions that can be modeled by mixed integer linear programming (MILP) techniques. Under these methods, piecewise linear functions describe nonlinearities and bi- nary variables … Read more
It has been recently proven that the semidefinite programming (SDP) relaxation of the optimal power flow problem over radial networks is exact under technical conditions such as not including generation lower bounds or allowing load over-satisfaction. In this paper, we investigate the situation where generation lower bounds are present. We show that even for a … Read more
In this work we consider the uniform capacitated single-item single-machine lot-sizing problem with continuous start-up costs. A continuous start-up cost is generated in a period whenever there is a nonzero production in the period and the production capacity in the previous period is not saturated. This concept of start-up does not correspond to the standard … Read more