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Many power systems operation and planning computations (e.g., transmission and generation switching and placement) solve a mixed-integer nonlinear problem (MINLP) with binary variables representing the decision to connect devices to the…
Mixed integer bilinear programs (MIBLPs) offer tools to resolve robotics motion planning problems with orthogonal rotation matrices or static moment balance, but require long solving times. Recent work utilizing data-driven methods has…
Autonomous agents are limited in their ability to observe the world state. Partially observable Markov decision processes (POMDPs) formally model the problem of planning under world state uncertainty, but POMDPs with continuous actions and…
Decentralized planning in uncertain environments is a complex task generally dealt with by using a decision-theoretic approach, mainly through the framework of Decentralized Partially Observable Markov Decision Processes (DEC-POMDPs).…
Protected areas (PAs) are designated spaces where human activities are restricted to preserve critical habitats. Decision-makers are challenged with balancing a trade-off of financial feasibility with ecological benefit when establishing…
Minimum distance constraints (minDCs) appear in many geometric optimization problems. They pose major challenges for mixed-integer nonlinear programming (MINLP) due to their reverse-convexity. We develop new algorithms for tightening…
This work attempts to combine the strengths of two major technologies that have matured over the last three decades: global mixed-integer nonlinear optimization and branch-and-price. We consider a class of generally nonconvex mixed-integer…
Mixed integer nonlinear programming (MINLP) problems are encountered in modeling a physical/industrial process consisting both nonlinearity and discrete selective parameters. There are variety of algorithms for solving MINLP problems most…
A large class of decision making under uncertainty problems can be described via Markov decision processes (MDPs) or partially observable MDPs (POMDPs), with application to artificial intelligence and operations research, among others.…
In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…
While mixed-integer linear programming and convex programming solvers have advanced significantly over the past several decades, solution technologies for general mixed-integer nonlinear programs (MINLPs) have yet to reach the same level of…
The optimal selection, sizing, and location of small-scale technologies within a grid-connected distributed energy system (DES) can contribute to reducing carbon emissions, consumer costs, and network imbalances. This is the first study to…
Numerous real-world decision-making problems can be formulated and solved using Mixed-Integer Linear Programming (MILP) models. However, the transformation of these problems into MILP models heavily relies on expertise in operations…
Mixed-integer nonlinear programs (MINLPs) arise in domains such as energy systems, process engineering, and transportation, and are notoriously difficult to solve at scale due to the interplay of discrete decisions and nonlinear…
Energy systems planning models identify least-cost strategies for expansion and operation of energy systems and provide decision support for investment, planning, regulation, and policy. Most are formulated as linear programming (LP) or…
We consider the problem of designing policies for Markov decision processes (MDPs) with dynamic coherent risk objectives and constraints. We begin by formulating the problem in a Lagrangian framework. Under the assumption that the risk…
This paper proposes a joint decomposition method that combines La- grangian decomposition and generalized Benders decomposition, to efficiently solve multiscenario nonconvex mixed-integer nonlinear programming (MINLP) problems to global…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
Planning under uncertainty is a central problem in the study of automated sequential decision making, and has been addressed by researchers in many different fields, including AI planning, decision analysis, operations research, control…
Stochastic programming provides a natural framework for modeling sequential optimization problems under uncertainty; however, the efficient solution of large-scale multistage stochastic programs remains a challenge, especially in the…