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Decades of advances in mixed-integer linear programming (MILP) and recent development in mixed-integer second-order-cone programming (MISOCP) have translated very mildly to progresses in global solving nonconvex mixed-integer quadratically…
This article describes the methodology for formulating and solving optimal pump scheduling problems with variable-speed pumps (VSPs) as mixed integer linear programs (MILPs) using piece-linear approximations of the network components. The…
In recent work, robust Principal Components Analysis (PCA) has been posed as a problem of recovering a low-rank matrix $\mathbf{L}$ and a sparse matrix $\mathbf{S}$ from their sum, $\mathbf{M}:= \mathbf{L} + \mathbf{S}$ and a provably exact…
We consider the Sparse Principal Component Analysis (SPCA) problem under the well-known spiked covariance model. Recent work has shown that the SPCA problem can be reformulated as a Mixed Integer Program (MIP) and can be solved to global…
Mixed-integer linear programming (MILP) has been a fundamental problem in combinatorial optimization. Conventional MILP solving mainly relies on carefully designed heuristics embedded in the branch-and-bound framework. Driven by the strong…
Principal component analysis (PCA) is one of the most widely used dimensionality reduction tools in data analysis. The PCA direction is a linear combination of all features with nonzero loadings -- this impedes interpretability. Sparse PCA…
Mixed-integer convex programming (MICP) has seen significant algorithmic and hardware improvements with several orders of magnitude solve time speedups compared to 25 years ago. Despite these advances, MICP has been rarely applied to…
In many operational applications, it is necessary to routinely find, within a very limited time window, provably good solutions to challenging mixed-integer linear programming (MILP) problems. An example is the Security-Constrained Unit…
Proportional-integral-derivative (PID) control, the most common control strategy in the industry, always suffers from health problems resulting from external disturbances, improper tuning, etc. Therefore, there have been many studies on…
A mathematical program for global optimization of the cable layout of Offshore Wind Farms (OWFs) is presented. The model consists on a Mixed Integer Linear Program (MILP). Modern branch-and-cut solvers are able to solve large-scale…
Navigating rigid body objects through crowded environments can be challenging, especially when narrow passages are presented. Existing sampling-based planners and optimization-based methods like mixed integer linear programming (MILP)…
The problem of optimal motion planing and control is fundamental in robotics. However, this problem is intractable for continuous-time stochastic systems in general and the solution is difficult to approximate if non-instantaneous nonlinear…
Combinatorial optimisation problems framed as mixed integer linear programmes (MILPs) are ubiquitous across a range of real-world applications. The canonical branch-and-bound algorithm seeks to exactly solve MILPs by constructing a search…
In this workshop, we discuss several algorithms for mathematical programs with equilibrium constraints (MPECs). The unifying theme is that MPECs are optimization problems whose feasible set contains a lower-level equilibrium system, often…
Cutting planes are crucial in solving mixed integer linear programs (MILP) as they facilitate bound improvements on the optimal solution. Modern MILP solvers rely on a variety of separators to generate a diverse set of cutting planes by…
This work presents a data-driven method for approximation of the maximum positively invariant (MPI) set and the maximum controlled invariant (MCI) set for nonlinear dynamical systems. The method only requires the knowledge of a finite…
Mixed Integer Linear Programming (MILP) is a fundamental tool for modeling combinatorial optimization problems. Recently, a growing body of research has used machine learning to accelerate MILP solving. Despite the increasing popularity of…
Fast and accurate large-scale energy system models are needed to investigate the potential of storage to complement the fluctuating energy production of renewable energy systems. However, standard Mixed-Integer Programming (MIP) models that…
Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we…
In this paper, we consider the multiple probabilistic covering location problem (MPCLP), which attempts to open a fixed number of facilities to maximize the total covered customer demand under a joint probabilistic coverage setting. We…