The solver DICOPT is based on an outer-approximation algorithm used for solving mixed- integer nonlinear programming (MINLP) problems. This algorithm is very effective for solving some types of convex MINLPs. However, there are certain problems that are dicult to solve with this algorithm. One of these problems is when the nonlinear constraints are so restrictive … Read more
To deliver to consumers in densely populated urban areas, companies often employ a two-echelon logistics system. In a two-echelon logistics system, the entry point for goods to be delivered in the urban area is a city distribution center (CDC). From a CDC the goods are transported to an intermediate facility, from where the goods are … Read more
The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the quadratic shortest path problem with a matrix variable of order $m+1$, where $m$ is … Read more
Testing a given matrix for membership in the family of Bernoulli matrices is a longstanding problem, the many applications of Bernoulli vectors in computer science, finance, medicine, and operations research emphasize its practical relevance. A novel approach towards this problem was taken by [Fiebig et al., 2017] for lowdimensional settings d
Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control over the desired level of sparsity of estimators. We analyze its structural properties and in doing … Read more
We investigate methods to solve the maximum-reliability stochastic network interdiction problem (SNIP). In this problem, a defender interdicts arcs on a directed graph to minimize an attacker’s probability of undetected traversal through the network. The attacker’s origin and destination are unknown to the defender and assumed to be random. SNIP can be formulated as a … Read more
In this paper, we consider the problem of identifying the type (local minimizer, maximizer or saddle point) of a given isolated real critical point $c$, which is degenerate, of a multivariate polynomial function $f$. To this end, we introduce the definition of faithful radius of $c$ by means of the curve of tangency of $f$. … Read more
We propose a global optimization algorithm for stochastic nonlinear programs that uses a specialized spatial branch and bound (BB) strategy to exploit the nearly decomposable structure of the problem. In particular, at each node in the BB scheme, a lower bound is constructed by relaxing the so-called non-anticipativity constraints and an upper bound is constructed … Read more
The unconstrained minimization of a sufficiently smooth objective function $f(x)$ is considered, for which derivatives up to order $p$, $p\geq 2$, are assumed to be available. An adaptive regularization algorithm is proposed that uses Taylor models of the objective of order $p$ and that is guaranteed to find a first- and second-order critical point in … Read more
This paper addresses the long-term planning of electric power infrastructures considering high renewable penetration. To capture the intermittency of these sources, we propose a deterministic multi-scale Mixed-Integer Linear Programming (MILP) formulation that simultaneously considers annual generation investment decisions and hourly operational decisions. We adopt judicious approximations and aggregations to improve its tractability. Moreover, to overcome … Read more