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We study the convex hull of the intersection of a convex set E and a disjunctive set. This intersection is at the core of solution techniques for Mixed Integer Convex Optimization. We prove that if there exists a cone K (resp., a cylinder C) that has the same intersection with the boundary of the disjunction as E , then the convex hull is the intersection… (More)

- Pietro Belotti, Julio C. Góez, Imre Pólik, Ted K. Ralphs, Tamás Terlaky
- Discrete Applied Mathematics
- 2013

In this paper we investigate families of quadrics that have fixed intersections with two given hyperplanes. The cases when the two hyperplanes are parallel and when they are nonparallel are discussed. We show that these families can be described with only one parameter. In particular we show how the quadrics are transformed as the parameter changes. This… (More)

We investigate the derivation of disjunctive conic cuts for mixed integer second order cone optimization (MISOCO). These conic cuts characterize the convex hull of the intersection of a disjunctive set and the feasible set of a MISOCO problem. We present a full characterization of these inequalities when the disjunctive set considered is defined by parallel… (More)

- Pietro Belotti, Julio C. Góez, Imre Pólik, Ted K. Ralphs, Tamás Terlaky
- Discrete Optimization
- 2017

We study the convex hull of the intersection of a disjunctive set defined by parallel hyperplanes and the feasible set of a mixed integer second order cone optimization (MISOCO) problem. We extend our prior work on disjunctive conic cuts (DCCs), which has thus far been restricted to the case in which the intersection of the hyperplanes and the feasible set… (More)

- Juan F. Pérez, Daniel F. Silva, +4 authors Germán Riaño
- ACM Trans. Math. Softw.
- 2017

Markov chains (MC) are a powerful tool for modeling complex stochastic systems. Whereas a number of tools exist for <i>solving</i> different types of MC models, the first step in MC modeling is to define the model parameters. This step is, however, error prone and far from trivial when modeling complex systems. In this article, we introduce jMarkov, a… (More)

The unit commitment problem is to find the production scheduling of a set of electric power generating units, and the generation levels for each unit, over a short term, typically from 24 hours to one week. The objective is to find the optimal schedule which meets the energy demand forecast at a minimum cost, and satisfy technological constraints such as… (More)

- Marco Cote, Germán Riaño, Raha Akhavan-Tabatabaei, Juan F. Pérez, Andrés Sarmiento, Julio C. Góez
- SIGMETRICS Performance Evaluation Review
- 2012

When analyzing real life stochastic systems in most cases is easier, cheaper and more effective to use analytical models rather than studying the physical system or a simulation model of it. The stochastic modeling is a powerful tool that helps the analysis and optimization of stochastic systems.
However the use of stochastic modeling is not widely spread… (More)

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