Mixed-Projection Conic Optimization: A New Paradigm for Modeling Rank Constraints

Projection methods in conic optimization

There exist efficient algorithms to project a point onto the intersection of a convex cone and an affine subspace. Those conic projections are in turn the work-horse of a range of algorithms in conic optimization, having a variety of applications in science, finance and engineering. This chapter reviews some of these algorithms, emphasizing the so-called regularization algorithms for linear con...

-Duality Theorems for Convex Semidefinite Optimization Problems with Conic Constraints

Disjunctive Conic Cuts for Mixed Integer Second Order Cone Optimization

We investigate the derivation of disjunctive conic cuts for mixed integer second order cone optimization (MISOCO). These conic cuts characterize the convex hull of the intersection of a disjunctive set and the feasible set of a MISOCO problem. We present a full characterization of these inequalities when the disjunctive set considered is defined by parallel hyperplanes.

A New Paradigm for Groundwater Modeling

We present in this paper an innovative and sophisticated software environment, called Interactive Groundwater (IGW), for unified deterministic and stochastic groundwater modeling. Based on a set of efficient and robust computational algorithms, IGW allows simulating complex, 3D unsteady flow and solute transport in saturated porous media subject to both systematic and “random” stresses and geol...

Submodularity in Conic Quadratic Mixed 0-1 Optimization

We describe strong convex valid inequalities for conic quadratic mixed 0-1 optimization. The inequalities exploit the submodularity of the binary restrictions and are based on the polymatroid inequalities over binaries for the diagonal case. We prove that the convex inequalities completely describe the convex hull of a single conic quadratic constraint as well as the rotated cone constraint ove...