4 papers
A polynomial-time solvable class of sparse box-constrained polynomial optimization problems
Aida Khajavirad
We study the problem of minimizing a multivariate polynomial function over the unit hypercube. Exploiting sparsity in the interaction graph or hypergraph, we identify variables tha…
Tight semidefinite programming relaxations for sparse box-constrained quadratic programs
Aida Khajavirad
We introduce a new class of semidefinite programming (SDP) relaxations for sparse box-constrained quadratic programs, obtained by a novel integration of the Reformulation Lineariza…
A second-order cone representable class of nonconvex quadratic programs
Santanu S. Dey, Aida Khajavirad
We consider the problem of minimizing a sparse nonconvex quadratic function over the unit hypercube. By developing an extension of the Reformulation-Linearization Technique (RLT) t…
The circle packing problem: a theoretical comparison of various convexification techniques
Aida Khajavirad
We consider the problem of packing congruent circles with the maximum radius in a unit square as a mathematical optimization problem. Due to the presence of non-overlapping constra…