A constructive characterization of the split closure of a mixed integer linear program

Two independent proofs of the polyhedrality of the split closure of mixed integer linear program have been previously presented. Unfortunately neither of these proofs is constructive. In this paper, we present a constructive version of this proof. We also show that split cuts dominate a family of inequalities introduced by Köppe and Weismantel.     

Convex hull of two quadratic or a conic quadratic and a quadratic inequality

Mathematical Programming - In this paper we consider an aggregation technique introduced by Yıldıran (J Math Control Inf 26:417–450, 2009) to study the convex hull of regions...     

Extended formulations in mixed integer conic quadratic programming

In this paper we consider the use of extended formulations in LP-based algorithms for mixed integer conic quadratic programming (MICQP). Extended formulations have been used by Vielma et al. (INFORMS J Comput 20: 438–450, 2008) and Hijazi et al. (Comput Optim Appl 52: 537–558, 2012) to construct algorithms for MICQP that can provide a significant computational advantage. The first approach is based on an extended or lifted polyhedral relaxation of the Lorentz cone by Ben-Tal and Nemirovski (Math Oper Res 26(2): 193–205 2001) that is extremely economical, but whose approximation quality cannot be iteratively improved. The second is based on a lifted polyhedral relaxation of the euclidean ball that can be constructed using techniques introduced by Tawarmalani and Sahinidis (Math Programm 103(2): 225–249, 2005). This relaxation is less economical, but its approximation quality can be iteratively improved. Unfortunately, while the approach of Vielma, Ahmed and Nemhauser is applicable for general MICQP problems, the approach of Hijazi, Bonami and Ouorou can only be used for MICQP problems with convex quadratic constraints. In this paper we show how a homogenization procedure can be combined with the technique by Tawarmalani and Sahinidis to adapt the extended formulation used by Hijazi, Bonami and Ouorou to a class of conic mixed integer programming problems that include general MICQP problems. We then compare the effectiveness of this new extended formulation against traditional and extended formulation-based algorithms for MICQP. We find that this new formulation can be used to improve various LP-based algorithms. In particular, the formulation provides an easy-to-implement procedure that, in our benchmarks, significantly improved the performance of commercial MICQP solvers.     

Optical absorption study of CuInTe2 crystals grown from near-stoichiometric compositions

From the optical absorption study of CuInTe₂ crystals grown from non-stoichiometric compositions, it has been shown that the sharp increase in the absorption coefficient observed around 0.90 eV corresponds to the transition between the shallow acceptor level and the conduction band and not due to the energy gap as reported earlier. The origin of this shallow acceptor state has been attributed to Te vacancy, which confirms the covalent bonding model for CuInTe₂.     

On-line determination of antimony(III) and antimony(V) in liver tissue and whole blood by flow injection - hydride generation - atomic absorption spectrometry

A new analytical procedure for the speciation of antimony in liver tissues is presented here. For this purpose, a flow injection system has been developed for the treatment of samples and the determination of antimony by hydride generation - atomic absorption spectrometry. The method involves the sequential and the on-line extraction of antimony(III) and antimony(V) from solid lyophilized blood and hamsters liver tissues, with 1.5 mol l(-1) acetic acid and 0.5 mol l(-1) sulfuric acid for Sb(III) and Sb(V), respectively. Reduction of Sb(V) to Sb(III) for stibine generation is effected by the on-line pre-reduction with l-cysteine. The linear ranges were 2.5-20 and 1.0-25 mug l(-1) of Sb(III) and Sb(V), respectively. The detection limits (3sigma) were 1.0 mug l(-1) for Sb(III) and 0.5 mug l(-1) for Sb(V). The relative standard deviation values for fifteen independent measurements were 2.1 and 1.8% for Sb(III) and Sb(V), respectively. The recovery studies performed with samples of cattle liver provided results from 98 to 100% for Sb(III) and from 100 to 103% for Sb(V) for samples spiked with single species. For samples spiked with both Sb(III) and Sb(V), the recovery varied from 97 to 103% for Sb(III) and from 101 to 103% for Sb(V).     

Disjunctive cuts in Mixed-Integer Conic Optimization

Mathematical Programming - This paper studies disjunctive cutting planes in Mixed-Integer Conic Programming. Building on conic duality, we formulate a cut-generating conic program for separating...     

Incremental and encoding formulations for Mixed Integer Programming

The standard way to represent a choice between n$n$ alternatives in Mixed Integer Programming is through n$n$ binary variables that add up to one. Unfortunately, this approach commonly leads to unbalanced branch-and-bound trees and diminished solver performance. In this paper, we present an encoding formulation framework that encompasses and expands existing approaches to mitigate this behavior. Through this framework, we generalize the incremental formulation for piecewise linear functions to any finite union of polyhedra with identical recession cones.     

On the Chvátal–Gomory closure of a compact convex set

In this paper, we show that the Chvátal–Gomory closure of any compact convex set is a rational polytope. This resolves an open question of Schrijver (Ann Discret Math 9:291–296, 1980) for irrational polytopes, and generalizes the same result for the case of rational polytopes (Schrijver in Ann Discret Math 9:291–296, 1980), rational ellipsoids (Dey and Vielma in IPCO XIV, Lecture Notes in Computer Science, vol 6080. Springer, Berlin, pp 327–340, 2010) and strictly convex bodies (Dadush et al. in Math Oper Res 36:227–239, 2011).