22 citations · 79 across the 19 of their papers we have counts for
24 papers
Optimization hierarchies for distance-avoiding sets in compact spaces
Bram Bekker, Olga Kuryatnikova, Fernando Mário de Oliveira Filho +1
Witsenhausen's problem asks for the maximum fraction of the -dimensional unit sphere that can be covered by a measurable set containing no pairs of orthogonal points. The…
Linear convergence of the Douglas-Rachford algorithm via a generic error bound condition
Javier Peña, Juan C. Vera, Luis F. Zuluaga
We provide new insight into the convergence properties of the Douglas-Rachford algorithm for the problem , where and are convex functions. Our approac…
Computing near-optimal Value-at-Risk portfolios using Integer Programming techniques
Onur Babat, Juan C. Vera, Luis F. Zuluaga
Value-at-Risk (VaR) is one of the main regulatory tools used for risk management purposes. However, it is difficult to compute optimal VaR portfolios; that is, an optimal risk-rewa…
Static Hedging of Weather and Price Risks in Electricity Markets
Javier Pantoja Robayo, Juan C. Vera
We present the closed-form solution to the problem of hedging price and quantity risks for energy retailers (ER), using financial instruments based on electricity price and weather…
The maximum -colorable subgraph problem and related problems
Renata Sotirov, Olga Kuryatnikova, Juan Vera
The maximum -colorable subgraph (MCS) problem is to find an induced -colorable subgraph with maximum cardinality in a given graph. This paper is an in-depth analysis of th…
Reducing non-negativity over general semialgebraic sets to non-negativity over simple sets
Olga Kuryatnikova, Juan C. Vera, Luis F. Zuluaga
A non-negativity certificate (NNC) is a way to write a polynomial so that its non-negativity on a semialgebraic set becomes evident. Positivstellensätze (Psätze) guarantee the exis…
Equivalence and invariance of the chi and Hoffman constants of a matrix
Javier F. Pena, Juan C. Vera, Luis F. Zuluaga
We show that the following two condition measures of a full column rank matrix are identical: the chi constant and a signed Hoffman constant. This id…
New characterizations of Hoffman constants for systems of linear constraints
Javier Pena, Juan Vera, Luis Zuluaga
We give a characterization of the Hoffman constant of a system of linear constraints in {\em relative} to a {\em reference polyhedron} . The reference polyhe…
Generalizations of Schoenberg's theorem on positive definite kernels
Olga Kuryatnikova, Juan C. Vera
The seminal theorem of I.J. Schoenberg characterizes positive definite (p.d.) kernels on the unit sphere invariant under the automorphisms of the sphere. We obtain two ge…
Positive semidefinite approximations to the cone of copositive kernels
Olga Kuryatnikova, Juan C. Vera
It has been shown that the maximum stable set problem in some infinite graphs, and the kissing number problem in particular, reduces to a minimization problem over the cone of copo…
Using Column Generation to Solve Extensions to the Markowitz Model
Lorenz M. Roebers, Aras Selvi, Juan C. Vera
We introduce a solution scheme for portfolio optimization problems with cardinality constraints. Typical portfolio optimization problems are extensions of the classical Markowitz m…
An algorithm to compute the Hoffman constant of a system of linear constraints
Javier Pena, Juan Vera, Luis Zuluaga
We propose a combinatorial algorithm to compute the Hoffman constant of a system of linear equations and inequalities. The algorithm is based on a characterization of the Hoffman c…
New bounds for truthful scheduling on two unrelated selfish machines
Olga Kuryatnikova, Juan C. Vera
We consider the minimum makespan problem for tasks and two unrelated parallel selfish machines. Let be the best approximation ratio of randomized monotone scale-free algo…
Positive polynomials on unbounded domains
Javer Pena, Juan C. Vera, Luis F. Zuluaga
Certificates of non-negativity such as Putinar's Positivstellensatz have been used to obtain powerful numerical techniques to solve polynomial optimization (PO) problems. Putinar's…
Computing semiparametric bounds on the expected payments of insurance instruments via column generation
Robert Howley, Robert Storer, Juan Vera +1
It has been recently shown that numerical semiparametric bounds on the expected payoff of fi- nancial or actuarial instruments can be computed using semidefinite programming. Howev…
Globally solving Non-Convex Quadratic Programs via Linear Integer Programming techniques
Wei Xia, Juan Vera, Luis F. Zuluaga
Quadratic programming (QP) is a well-studied fundamental NP-hard optimization problem which optimizes a quadratic objective over a set of linear constraints. In this paper, we refo…
On the convergence rate of grid search for polynomial optimization over the simplex
Etienne de Klerk, Monique Laurent, Zhao Sun +1
We consider the approximate minimization of a given polynomial on the standard simplex, obtained by taking the minimum value over all rational grid points with given denominator ${…
Improved Bounds on the Phase Transition for the Hard-Core Model in 2-Dimensions
Juan C. Vera, Eric Vigoda, Linji Yang
For the hard-core lattice gas model defined on independent sets weighted by an activity , we study the critical activity for the uniqueness/non-uniqueness th…
Phase Transition for Glauber Dynamics for Independent Sets on Regular Trees
Ricardo Restrepo, Daniel Stefankovic, Juan C. Vera +2
We study the effect of boundary conditions on the relaxation time of the Glauber dynamics for the hard-core model on the tree. The hard-core model is defined on the set of independ…
Phase transition for the mixing time of the Glauber dynamics for coloring regular trees
Prasad Tetali, Juan C. Vera, Eric Vigoda +1
We prove that the mixing time of the Glauber dynamics for random k-colorings of the complete tree with branching factor b undergoes a phase transition at . Ou…
Logconcave Random Graphs
Alan Frieze, Santosh Vempala, Juan Vera
We propose the following model of a random graph on n vertices. Let F be a distribution in R_+^{n(n-1)/2} with a coordinate for every pair i$ with 1 \le i,j \le n. Then G_{F,p} is…
Reconstruction for Colorings on Trees
Nayantara Bhatnagar, Juan Vera, Eric Vigoda +1
Consider -colorings of the complete tree of depth and branching factor . If we fix the coloring of the leaves, as tends to , for what range of is th…
Randomly coloring planar graphs with fewer colors than the maximum degree
Thomas P. Hayes, Juan C. Vera, Eric Vigoda
We study Markov chains for randomly sampling -colorings of a graph with maximum degree . Our main result is a polynomial upper bound on the mixing time of the single-site upd…
Bias reduction in traceroute sampling: towards a more accurate map of the Internet
Abraham D. Flaxman, Juan Vera
Traceroute sampling is an important technique in exploring the internet router graph and the autonomous system graph. Although it is one of the primary techniques used in calculati…