Andrés Gómez

Simplex QP-based methods for minimizing a conic quadratic objective over polyhedra

Categories Quadratic Programming, Robust Optimization, Second-Order Cone Programming Tags ,

We consider minimizing a conic quadratic objective over a polyhedron. Such problems arise in parametric value-at-risk minimization, portfolio optimization, and robust optimization with ellipsoidal objective uncertainty; and they can be solved by polynomial interior point algorithms for conic quadratic optimization. However, interior point algorithms are not well-suited for branch-and-bound algorithms for the discrete counterparts of … Read more

Maximizing a class of utility functions over the vertices of a polytope

Categories (Mixed) Integer Nonlinear Programming, Robust Optimization, Stochastic Programming Tags , , , , , , , ,

Given a polytope X, a monotone concave univariate function g, and two vectors c and d, we study the discrete optimization problem of finding a vertex of X that maximizes the utility function c’x + g(d’x). This problem has numerous applications in combinatorial optimization with a probabilistic objective, including estimation of project duration with stochastic … Read more