Necessary Conditions for the Impulsive Optimal Control of Multibody Mechanical Systems

In this work, necessary conditions for the impulsive optimal control of multibody mechanical systems are stated. The conditions are obtained by the application subdifferential calculus techniques to extended-valued lower semi-continuous generalized Bolza functional that is evaluated on multiple intervals. Contrary to the approach in literature so far, the instant of possibly impulsive transition is considered … Read more

Dynamic Subgradient Methods

Lagrangian relaxation is commonly used to generate bounds for mixed-integer linear programming problems. However, when the number of dualized constraints is very large (exponential in the dimension of the primal problem), explicit dualization is no longer possible. In order to reduce the dual dimension, different heuristics were proposed. They involve a separation procedure to dynamically … Read more

A Subspace Limited Memory BFGS Algorithm For Box Constrained Optimization

In this paper, a subspace limited BFGS algorithm is proposed for bound constrained optimization. The global convergence will be established under some suitable conditions. Numerical results show that this method is more competitive than the normal method does. Article Download View A Subspace Limited Memory BFGS Algorithm For Box Constrained Optimization

The Facility Location Problem with Bernoulli Demands

In this paper we address a discrete capacitated facility location problem in which customers have Bernoulli demands. The problem is formulated as a two-stage stochastic program. The goal is to define an a priori solution for the location of the facilities and for the allocation of customers to the operating facilities that minimize the expected … Read more

Projections Onto Super-Half-Spaces for Monotone Variational Inequality Problems in Finite-Dimensional Spaces

The variational inequality problem (VIP) is considered here. We present a general algorithmic scheme which employs projections onto hyperplanes that separate balls from the feasible set of the VIP instead of projections onto the feasible set itself. Our algorithmic scheme includes the classical projection method and Fukushima’s subgradient projection method as special cases. Citation Technical … Read more

An SDP-based divide-and-conquer algorithm for large scale noisy anchor-free graph realization

We propose the DISCO algorithm for graph realization in $\real^d$, given sparse and noisy short-range inter-vertex distances as inputs. Our divide-and-conquer algorithm works as follows. When a group has a sufficiently small number of vertices, the basis step is to form a graph realization by solving a semidefinite program. The recursive step is to break … Read more

Near-Optimal Solutions and Integrality Gaps for Almost All Instances of Single-Machine Precedence-Constrained Scheduling

We consider the problem of minimizing the weighted sum of completion times on a single machine subject to bipartite precedence constraints where all minimal jobs have unit processing time and zero weight, and all maximal jobs have zero processing time and unit weight. For various probability distributions over these instances–including the uniform distribution–we show several … Read more

Improved strategies for branching on general disjunctions

Within the context of solving Mixed-Integer Linear Programs by a Branch-and-Cut algorithm, we propose a new strategy for branching. Computational experiments show that, on the majority of our test instances, this approach enumerates fewer nodes than traditional branching. On average, on instances that contain both integer and continuous variables the number of nodes in the … Read more

Identification and Elimination of Interior Points for the Minimum Enclosing Ball Problem

Given $\cA := \{a^1,\ldots,a^m\} \subset \R^n$, we consider the problem of reducing the input set for the computation of the minimum enclosing ball of $\cA$. In this note, given an approximate solution to the minimum enclosing ball problem, we propose a simple procedure to identify and eliminate points in $\cA$ that are guaranteed to lie … Read more

A new library of structured semidefinite programming instances

Solvers for semidefinite programming (SDP) have evolved a great deal in the last decade, and their development continues. In order to further support and encourage this development, we present a new test set of SDP instances. These instances arise from recent applications of SDP in coding theory, computational geometry, graph theory and structural design. Most … Read more