In this paper, we establish a low-degree polynomially-sized reduction between tree
ensemble optimization and optimization of multilinear functions over a Cartesian product of …

In this paper, we consider piecewise polyhedral relaxations (PPRs) of multilinear
optimization problems over axis-parallel hyperrectangular partitions of their domain. We …

We present a novel idea of the membership function using logical expressions over
inequalities. This is achieved by introducing the multidimensional membership function …

We present a novel algorithm for separating facet-inducing inequalities for the convex-hull of
the union of polytopes representing a disjunctive constraint of special structure. It is required …

We introduce techniques to build small ideal mixed-integer programming (MIP) formulations
of combinatorial disjunctive constraints (CDCs) via the independent branching scheme. We …

Doctor of Philosophy Page 1 RICE UNIVERSITY By A THESIS SUBMITTED IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE APPROVED, THESIS …

In this thesis, we consider situations when optimization problems include objective and/or
constraint functions whose explicit forms are not directly available. We focus on two …