Related papers: Mixed-integer linearity in nonlinear optimization:…
In this paper, we provide the first provable linear-time (in the number of non-zero entries of the input) algorithm for approximately solving the generalized trust region subproblem (GTRS) of minimizing a quadratic function over a quadratic…
We study the representability of sets that admit extended formulations using mixed-integer bilevel programs. We show that feasible regions modeled by continuous bilevel constraints (with no integer variables), complementarity constraints,…
Adaptive regularized framework using cubics has emerged as an alternative to line-search and trust-region algorithms for smooth nonconvex optimization, with an optimal complexity amongst second-order methods. In this paper, we propose and…
Density functional theory calculations use a significant fraction of current supercomputing time. The resources required scale with the problem size, internal workings of the code and the number of iterations to convergence, the latter…
While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…
This paper proposes a tractable framework to determine key characteristics of non-linear dynamic systems by converting physics-informed neural networks to a mixed integer linear program. Our focus is on power system applications.…
The powertrain of battery electric vehicles can be optimized to maximize the travel distance for a given amount of stored energy in the traction battery. To achieve this, a combined control and design problem has to be solved which results…
In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the…
We address the multi-satellite scheduling problem with limited observation capacities that arises from the need to observe a set of targets on the Earth's surface using imaging resources installed on a set of satellites. We define and…
We present an augmented Lagrangian trust-region method to efficiently solve constrained optimization problems governed by large-scale nonlinear systems with application to partial differential equation-constrained optimization. At each…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
We present a new framework for solving general topology optimization (TO) problems that find an optimal material distribution within a design space to maximize the performance of a structure while satisfying design constraints. These…
In this paper we analyze a continuous version of the maximal covering location problem, in which the facilities are required to be interconnected by means of a graph structure in which two facilities are allowed to be linked if a given…
This work presents PANTR, an efficient solver for nonconvex constrained optimization problems, that is well-suited as an inner solver for an augmented Lagrangian method. The proposed scheme combines forward-backward iterations with…
This article presents the first mixed-integer linear programming (MILP)-based iterative algorithm to solve factorable mixed-integer nonlinear programs (MINLPs) with bounded, differentiable periodic functions to global optimality with an…
We propose a hierarchical architecture for efficiently computing high-quality solutions to structured mixed-integer programs (MIPs). To reduce computational effort, our approach decouples the original problem into a higher level problem and…
We present a novel relaxation framework for general mixed-integer nonlinear programming (MINLP) grounded in computational geometry. Our approach constructs polyhedral relaxations by convexifying finite sets of strategically chosen points,…
To mitigate the vulnerability of distribution grids to severe weather events, some electric utilities use preemptive de-energization as the primary line of defense, causing significant power outages. In such instances, networked microgrids…
This paper addresses the problem of managing rotational load shedding schedules for a power distribution network with multiple load zones. An integer optimization problem is formulated to find the optimal number and duration of planned…
We present strong mixed-integer programming (MIP) formulations for high-dimensional piecewise linear functions that correspond to trained neural networks. These formulations can be used for a number of important tasks, such as verifying…