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Background: Multi-collimator proton minibeam radiation therapy (MC-pMBRT) has recently emerged as a versatile technique for dose shaping, enabling peak-valley dose patterns in organs-at-risk (OAR) while maintaining a uniform dose…

Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…

We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection,…

In this paper, we propose a Bi-layer Predictionbased Reduction Branch (BP-RB) framework to speed up the process of finding a high-quality feasible solution for Mixed Integer Programming (MIP) problems. A graph convolutional network (GCN) is…

Machine Learning models are increasingly used for decision making, in particular in high-stakes applications such as credit scoring, medicine or recidivism prediction. However, there are growing concerns about these models with respect to…

Hypernetworks, neural networks that predict the parameters of another neural network, are powerful models that have been successfully used in diverse applications from image generation to multi-task learning. Unfortunately, existing…

This paper proposes an efficient adaptive variant of a quadratic penalty accelerated inexact proximal point (QP-AIPP) method proposed earlier by the authors. Both the QP-AIPP method and its variant solve linearly set constrained nonconvex…

In this paper, we develop a new formulation of changeover constraints for mixed integer programming problem (MIP) that emerges in solving a short-term production scheduling problem. The new model requires fewer constraints than the original…

We present an extensible software framework, hIPPYlib, for solution of large-scale deterministic and Bayesian inverse problems governed by partial differential equations (PDEs) with infinite-dimensional parameter fields (which are…

We study the problem of learning a linear model to set the reserve price in an auction, given contextual information, in order to maximize expected revenue from the seller side. First, we show that it is not possible to solve this problem…

This paper proposes a generic formulation that significantly expedites the training and deployment of image classification models, particularly under the scenarios of many image categories and high feature dimensions. As a defining…

Mixed-integer (MI) quadratic models subject to quadratic constraints, known as All-Quadratic MI Programs, constitute a challenging class of NP-complete optimization problems. The particular scenario of unbounded integers defines a subclass…

Multidimensional optimization problems where the objective function and the constraints are multiextremal non-differentiable Lipschitz functions (with unknown Lipschitz constants) and the feasible region is a finite collection of robust…

Multiple data views measured on the same set of participants is becoming more common and has the potential to deepen our understanding of many complex diseases by analyzing these different views simultaneously. Equally important, many of…

Convex optimization encompasses a wide range of optimization problems that contain many efficiently solvable subclasses. Interior point methods are currently the state-of-the-art approach for solving such problems, particularly effective…

There is a growing interest in the machine learning community in developing predictive algorithms that are "interpretable by design". Towards this end, recent work proposes to make interpretable decisions by sequentially asking…

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…

This paper develops a method to obtain the optimal value for the regularization coefficient in a general mixed-integer problem (MIP). This approach eliminates the cross-validation performed in the existing penalty techniques to obtain a…

Semi-Infinite Programming (SIP) has emerged as a powerful framework for modeling problems with infinite constraints, however, its theoretical development in the context of nonconvex and large-scale optimization remains limited. In this…

For almost two decades, mixed integer programming (MIP) solvers have used graph-based conflict analysis to learn from local infeasibilities during branch-and-bound search. In this paper, we improve MIP conflict analysis by instead using…