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math.OC2019
Optimizing Sparsity over Lattices and Semigroups
Iskander Aliev, Gennadiy Averkov, Jesús A. De Loera +1
Motivated by problems in optimization we study the sparsity of the solutions to systems of linear Diophantine equations and linear integer programs, i.e., the number of non-zero en…
math.OC2019
Second-order cone representable slices of the positive semidefinite cone of size three
Gennadiy Averkov
To demonstrate the discrepancy between second-order cone and semidefinite programming, Hamza Fawzi showed that the cone S_+^3 of symmetric positive semidefinite matrices of size 3…
math.OC2019
Convexification of box-constrained polynomial optimization problems via monomial patterns
Gennadiy Averkov, Benjamin Peters, Sebastian Sager
Convexification is a core technique in global polynomial optimization. Currently, there are two main approaches competing in theory and practice: the approach of nonlinear programm…