Mixed-Integer PDE-Constrained Optimal Control of Gas Networks

We develop a mixed-integer optimal control model with partial differential equation (PDE) constraints for gas transport networks, designed for controlling extreme state transitions, such as flow reversals. Our model shows how to combine binary compressor controls with PDE flow models. We model the flow of gas using a variant of the Euler equations, which we … Read more

Minotaur: A Mixed-Integer Nonlinear Optimization Toolkit

We present a flexible framework for general mixed-integer nonlinear programming (MINLP), called Minotaur, that enables both algorithm exploration and structure exploitation without compromising computational efficiency. This paper documents the concepts and classes in our framework and shows that our implementations of standard MINLP techniques are efficient compared with other state-of-the-art solvers. We then describe structure-exploiting … Read more

A Two-Level Approach to Large Mixed-Integer Programs with Application to Cogeneration in Energy-Efficient Buildings

We study a two-stage mixed-integer linear program (MILP) with more than 1 million binary variables in the second stage. We develop a two-level approach by constructing a semi-coarse model (coarsened with respect to variables) and a coarse model (coarsened with respect to both variables and constraints). We coarsen binary variables by selecting a small number … Read more

Regularizing Bilevel Nonlinear Programs by Lifting

This paper considers a bilevel nonlinear program (NLP) whose lower-level problem satisfies a linear independence constraint qualification (LICQ) and a strong second-order condition (SSOC). One would expect the resulting mathematical program with complementarity constraints (MPCC), whose constraints are the first-order optimality conditions of the lower-level NLP, to satisfy an MPEC-LICQ. We provide an example which … Read more

Mixed-Integer Nonlinear Optimization

Many optimal decision problems in scientific, engineering, and public sector applications involve both discrete decisions and nonlinear system dynamics that affect the quality of the final design or plan. These decision problems lead to mixed-integer nonlinear programming (MINLP) problems that combine the combinatorial difficulty of optimizing over discrete variable sets with the challenges of handling … Read more

Solving Mixed-Integer Nonlinear Programs by QP-Diving

We present a new tree-search algorithm for solving mixed-integer nonlinear programs (MINLPs). Rather than relying on computationally expensive nonlinear solves at every node of the branch-and-bound tree, our algorithm solves a quadratic approximation at every node. We show that the resulting algorithm retains global convergence properties for convex MINLPs, and we present numerical results on … Read more

Optimal Response to Epidemics and Cyber Attacks in Networks

This paper introduces novel formulations for optimally responding to epidemics and cyber attacks in networks. In our models, at a given time period, network nodes (e.g., users or computing resources) are associated with probabilities of being infected, and each network edge is associated with some probability of propagating the infection. A decision maker would like … Read more

TACO – A Toolkit for AMPL Control Optimization

We describe a set of extensions to the AMPL modeling language to conveniently model mixed-integer optimal control problems for ODE or DAE dynamic processes. These extensions are realized as AMPL user functions and suffixes and do not require intrusive changes to the AMPL language standard or implementation itself. We describe and provide TACO, a Toolkit … Read more

More Branch-and-Bound Experiments in Convex Nonlinear Integer Programming

Branch-and-Bound (B&B) is perhaps the most fundamental algorithm for the global solution of convex Mixed-Integer Nonlinear Programming (MINLP) problems. It is well-known that carrying out branching in a non-simplistic manner can greatly enhance the practicality of B&B in the context of Mixed-Integer Linear Programming (MILP). No detailed study of branching has heretofore been carried out … Read more


We present a proactive energy management framework that integrates predictive dynamic building models and day-ahead forecasts of disturbances affecting efficiency and costs. This enables an efficient management of resources and an accurate prediction of the daily electricity demand profile. The strategy is based on the on-line solution of mixed-integer nonlinear programming problems. The framework is … Read more