We study mixed integer conic sets involving a general regular (closed, convex, full dimensional, and pointed) cone K such as the nonnegative orthant, the Lorentz cone or the positive semidefinite cone. In a unified framework, we introduce K-minimal inequalities and show that under mild assumptions, these inequalities together with the trivial cone-implied inequalities are sufficient … Read more
This paper concerns the method of selecting the best subset of explanatory variables in a multiple linear regression model. To evaluate a subset regression model, some goodness-of-fit measures, e.g., adjusted R^2, AIC and BIC, are generally employed. Although variable selection is usually handled via a stepwise regression method, the method does not always provide the … Read more
Mixed Integer Nonlinear Programming (MINLP) techniques are increasingly used to address challenging problems in robotics, especially Multi-Vehicle Motion Planning (MVMP). The main contribution of this paper is a discrete time-distributed Receding Horizon Mixed Integer Nonlinear Programming (RH-MINLP) formulation of the underwater multi-vehicle path coordination problem with constraints on kinematics, dynamics, collision avoidance, and acoustic communication … Read more
Let $C$ be a full-dimensional pointed closed convex cone in $R^m$ obtained by taking the conic hull of a strictly convex set. Given $A \in Q^{m \times n_1}$, $B \in Q^{m \times n_2}$ and $b \in Q^m$, a simple conic mixed-integer set (SCMIS) is a set of the form $\{(x,y)\in Z^{n_1} \times R^{n_2}\,|\,\ Ax +By … Read more
Motivated by mixed-integer, nonlinear optimization problems, we derive linear inequality characterizations for sets of the form conv{(x, q ) \in R^d × R : q \in Q(x), x \in R^d – int(P )} where Q is convex and differentiable and P \subset R^d . We show that in several cases our characterization leads to polynomial-time … Read more
The $pq$-relaxation for the pooling problem can be constructed by applying McCormick envelopes for each of the bilinear terms appearing in the so-called $pq$-formulation of the pooling problem. This relaxation can be strengthened by using piecewise-linear functions that over- and under-estimate each bilinear term. The resulting relaxation can be written as a mixed integer linear … Read more
We consider models of two-stage stochastic programming with a quantile second stage criterion and optimization models with a chance constraint on the second stage objective function values. Such models allow to formalize requirements to reliability and safety of the system under consideration, and to optimize the system in extreme conditions. We suggest a method of … Read more
In this paper, we consider mixed integer linear programming (MIP) formulations for piecewise linear functions (PLFs) that are evaluated when an indicator variable is turned on. We describe modifications to standard MIP formulations for PLFs with desirable theoretical properties and superior computational performance in this context. CitationTechnical Report #1788, Computer Sciences Department, University of Wisconsin-Madison.ArticleDownload … Read more
We suggest a method for equivalent transformation of a quantile optimization problem with discrete distribution of random parameters to mixed integer programming problems. The number of additional integer (in fact boolean) variables in the equivalent problems equals to the number of possible scenarios for random data. The obtained mixed integer problems are solved by standard … Read more
Balas introduced intersection cuts for mixed integer linear sets. Intersection cuts are given by closed form formulas and form an important class of cuts for solving mixed integer linear programs. In this paper we introduce an extension of intersection cuts to mixed integer conic quadratic sets. We identify the formula for the conic quadratic intersection … Read more