Christian Bingane

activity

20182022

most citedTight-and-cheap conic relaxation for the optimal reactive power dispatch problem

58 citations · 86 across the 9 of their papers we have counts for

collaborators

10 papers

math.MG2022

Small polygons with large area

Christian Bingane, Michael J. Mossinghoff

A polygon is \textit{small} if it has unit diameter. The maximal area of a small polygon with a fixed number of sides $n$ is not known when $n$ is even and $n \geq 14$ . We determine…

math.CO2021★ 5 cited

Tight bounds on the maximal area of small polygons: Improved Mossinghoff polygons

Christian Bingane

A small polygon is a polygon of unit diameter. The maximal area of a small polygon with $n = 2 m$ vertices is not known when $m \geq 7$ . In this paper, we construct, for each $n = 2 m$ an…

math.MG2021★ 2 cited

The equilateral small octagon of maximal width

Christian Bingane, Charles Audet

A small polygon is a polygon of unit diameter. The maximal width of an equilateral small polygon with $n = 2^{s}$ vertices is not known when $s \geq 3$ . This paper solves the first open…

math.MG2021★ 1 cited

Maximal perimeter and maximal width of a convex small polygon

Christian Bingane

A small polygon is a polygon of unit diameter. The maximal perimeter and the maximal width of a convex small polygon with $n = 2^{s}$ sides are unknown when $s \geq 4$ . In this paper, w…

math.OC2021★ 2 cited

Tight bounds on the maximal perimeter of convex equilateral small polygons

Christian Bingane, Charles Audet

A small polygon is a polygon that has diameter one. The maximal perimeter of a convex equilateral small polygon with $n = 2^{s}$ sides is not known when $s \geq 4$ . In this paper, we co…

math.OC2020★ 8 cited

Tight bounds on the maximal perimeter and the maximal width of convex small polygons

Christian Bingane

A small polygon is a polygon of unit diameter. The maximal perimeter and the maximal width of a convex small polygon with $n = 2^{s}$ vertices are not known when $s \geq 4$ . In this pap…

math.OC2020★ 3 cited

Largest small polygons: A sequential convex optimization approach

Christian Bingane

A small polygon is a polygon of unit diameter. The maximal area of a small polygon with $n = 2 m$ vertices is not known when $m \geq 7$ . Finding the largest small $n$ -gon for a given nu…

math.OC2019

Tight-and-cheap conic relaxation for the AC optimal power flow problem

Christian Bingane, Miguel F. Anjos, Sébastien Le Digabel

The classical alternating current optimal power flow problem is highly nonconvex and generally hard to solve. Convex relaxations, in particular semidefinite, second-order cone, con…

math.OC2019★ 7 cited

CONICOPF: Conic relaxations for AC optimal power flow computations

Christian Bingane, Miguel F. Anjos, Sébastien Le Digabel

Computational speed and global optimality are key needs for practical algorithms for the optimal power flow problem. Two convex relaxations offer a favorable trade-off between the…

math.OC2018★ 58 cited

Tight-and-cheap conic relaxation for the optimal reactive power dispatch problem

Christian Bingane, Miguel F. Anjos, Sébastien Le Digabel

The optimal reactive power dispatch (ORPD) problem is an alternating current optimal power flow (ACOPF) problem where discrete control devices for regulating the reactive power, su…