Results 1 to 10 of about 19,569 (69)

Lifts of convex sets and cone factorizations [PDF]

, 2012
In this paper we address the basic geometric question of when a given convex set is the image under a linear map of an affine slice of a given closed convex cone.
Barvinok A, Baston VJD, Ben-Tal A, João Gouveia, Marshall M, Pablo A. Parrilo, Rekha R. Thomas   +6 more
core   +4 more sources

Bad semidefinite programs: they all look the same [PDF]

, 2017
Conic linear programs, among them semidefinite programs, often behave pathologically: the optimal values of the primal and dual programs may differ, and may not be attained. We present a novel analysis of these pathological behaviors.
Bauschke H., Borwein J. M., Borwein J. M., Duffin R. J., Gábor Pataki, Lourenco B., Pataki G.   +6 more
core   +3 more sources

Exponential Lower Bounds for Polytopes in Combinatorial Optimization [PDF]

, 2015
We solve a 20-year old problem posed by Yannakakis and prove that there exists no polynomial-size linear program (LP) whose associated polytope projects to the traveling salesman polytope, even if the LP is not required to be symmetric.
de Wolf, Ronald, Fiorini, Samuel, Massar, Serge, Pokutta, Sebastian, Tiwary, Hans Raj   +4 more
core   +4 more sources

Recovery of binary sparse signals from compressed linear measurements via polynomial optimization [PDF]

, 2019
The recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics.
Abuabiah, Mohammad, Fosson, Sophie M.
core   +2 more sources

\(E\)-Convex programming

Journal of Numerical Analysis and Approximation Theory, 2004
In [6] one shows that some of the results obtained in [5] on \(E\)-convex programming are incorrect. In this paper we recover these results in the new hypotheses.
Liana Lupşa, Dorel Duca
doaj   +2 more sources

Equivalent relaxations of optimal power flow [PDF]

, 2014
Several convex relaxations of the optimal power flow (OPF) problem have recently been developed using both bus injection models and branch flow models.
Bose, Subhonmesh, Hassibi, Babak, Low, Steven H., Teeraratkul, Thanchanok   +3 more
core   +3 more sources

Polytopes of Minimum Positive Semidefinite Rank

, 2013
The positive semidefinite (psd) rank of a polytope is the smallest $k$ for which the cone of $k \times k$ real symmetric psd matrices admits an affine slice that projects onto the polytope.
Gouveia, João, Robinson, Richard Z., Thomas, Rekha R.   +2 more
core   +1 more source

Small Extended Formulations for Cyclic Polytopes

, 2015
We provide an extended formulation of size O(log n)^{\lfloor d/2 \rfloor} for the cyclic polytope with dimension d and n vertices (i,i^2,\ldots,i^d), i in [n]. First, we find an extended formulation of size log(n) for d= 2. Then, we use this as base case
Bogomolov, Yuri, Fiorini, Samuel, Maksimenko, Aleksandr, Pashkovich, Kanstantsin   +3 more
core   +1 more source

Learning Control Barrier Functions from Expert Demonstrations

, 2020
Inspired by the success of imitation and inverse reinforcement learning in replicating expert behavior through optimal control, we propose a learning based approach to safe controller synthesis based on control barrier functions (CBFs).
Dimarogonas, Dimos V., Hu, Haimin, Lindemann, Lars, Matni, Nikolai, Robey, Alexander, Tu, Stephen, Zhang, Hanwen   +6 more
core   +1 more source

Polynomial tuning of multiparametric combinatorial samplers

, 2017
Boltzmann samplers and the recursive method are prominent algorithmic frameworks for the approximate-size and exact-size random generation of large combinatorial structures, such as maps, tilings, RNA sequences or various tree-like structures.
Bendkowski, Maciej, Bodini, Olivier, Dovgal, Sergey   +2 more
core   +1 more source