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Efficient Interior-Point Methods for Hyperbolic Programming via Straight-Line Programs
Mehdi Karimi, Levent Tuncel
Hyperbolic (HB) programming generalizes many popular convex optimization problems, including semidefinite and second-order cone programming. Despite substantial theoretical progres…
Normalizations of factorizations over convex cones and their effects on extension complexity
Adam Brown, Kanstantsin Pashkovich, Levent Tunçel
Factorizations over cones and their duals play central roles for many areas of mathematics and computer science. One of the reasons behind this is the ability to find a representat…
Everything is possible: constructing spectrahedra with prescribed facial dimensions
Vera Roshchina, Levent Tunçel
Given any finite set of nonnegative integers, there exists a closed convex set whose facial dimension signature coincides with this set of integers, that is, the dimensions of its…
A Primal-Dual Extension of the Goemans--Williamson Algorithm for the Weighted Fractional Cut-Covering Problem
Nathan Benedetto Proença, Marcel K. de Carli Silva, Cristiane M. Sato +1
We study a weighted generalization of the fractional cut-covering problem, which we relate to the maximum cut problem via antiblocker and gauge duality. This relationship allows us…
Dyadic linear programming and extensions
Ahmad Abdi, Gérard Cornuéjols, Bertrand Guenin +1
A rational number is dyadic if it has a finite binary representation , where is an integer and is a nonnegative integer. Dyadic rationals are important for numerical…