4 papers
On the convexification of a bilinearly constrained set with a common variable
Hyun-Ju Oh, Boshi Yang
We study the convexification of sets defined by box constraints and bilinear inequality constraints in which all bilinear terms share a common variable. For this structured class o…
Quadratic Convexification of a Square Truncated by a Hyperbola
Yipeng Zhang, Yuyuan Ouyang, Boshi Yang
We study the quadratic convexification of the compact nonconvex set which is a square truncated by…
Nonnegative Quadratics over a Quadrant with a Bilinear Constraint
Yipeng Zhang, Yuyuan Ouyang, Boshi Yang
We study quadratic polynomials that are nonnegative on the non-compact set \[ F:=\{(x_1,x_2)\in\mathbb R^2:\ x_1\ge 0,\ x_2\ge 0,\ x_1x_2\le 1\}. \] All extreme rays of the cone of…
Pricing Discrete and Nonlinear Markets With Semidefinite Relaxations
Cheng Guo, Lauren Henderson, Ryan Cory-Wright +1
Nonconvexities in markets with discrete decisions and nonlinear constraints make efficient pricing challenging, often necessitating subsidies. A prime example is the unit commitmen…