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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…

Linear Predictive Clustering (LPC) partitions samples based on shared linear relationships between feature and target variables, with numerous applications including marketing, medicine, and education. Greedy optimization methods, commonly…

This paper presents a novel approach to the joint optimization of job scheduling and data allocation in grid computing environments. We formulate this joint optimization problem as a mixed integer quadratically constrained program. To…

The Maximum Balanced Biclique Problem (MBBP) is a prominent model with numerous applications. Yet, the problem is NP-hard and thus computationally challenging. We propose novel ideas for designing effective exact algorithms for MBBP.…

In this paper, we consider the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network resources to meet diverse…

We present a direct numerical method for the solution of an optimal control problem controlling the growth of LDL, HDL and plaque. The optimal control problem is constrained with a system of coupled nonlinear free and mixed boundary partial…

The minimum sum-of-squares clustering (MSSC), or k-means type clustering, has been recently extended to exploit prior knowledge on the cardinality of each cluster. Such knowledge is used to increase performance as well as solution quality.…

For elliptic interface problems with discontinuous coefficients, the maximum accuracy order for compact 9-point finite difference scheme in irregular points is three [7]. The discontinuous coefficients usually have abrupt jumps across the…

Governments across the world are planning to increase the share of renewables in their energy systems. The siting of new wind and solar power plants requires close coordination with grid planning, and hence co-optimization of investment in…

We propose a supervised learning framework for computing solutions of multi-parametric Mixed Integer Linear Programs (MILPs) that arise in Model Predictive Control. Our approach also quantifies sub-optimality for the computed solutions.…

The Cell Formation Problem has been studied as an optimization problem in manufacturing for more than 90 years. It consists of grouping machines and parts into manufacturing cells in order to maximize loading of cells and minimize movement…

We present a new multi-layer peeling technique to cluster points in a metric space. A well-known non-parametric objective is to embed the metric space into a simpler structured metric space such as a line (i.e., Linear Arrangement) or a…

Outer-approximation-based branch-and-bound is a common algorithmic framework for solving MINLPs (mixed-integer nonlinear programs) to global optimality, with branching variable selection critically influencing overall performance. In modern…

We extend the classical primal-dual interior point method from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior point method, is for solving Riemannian constrained optimization problems. We establish…

Point cloud alignment is a common problem in computer vision and robotics, with applications ranging from 3D object recognition to reconstruction. We propose a novel approach to the alignment problem that utilizes Bayesian nonparametrics to…

New algorithms are presented for numerical conformal mapping based on rational approximations and the solution of Dirichlet problems by least-squares fitting on the boundary. The methods are targeted at regions with corners, where the…

This paper addresses the problem of motion planning for differential drive micro-mobility platforms. This class of vehicle is designed to perform small-distance transportation of passengers and goods in structured environments. Our approach…

Bringing together nonlinear optimization with polyhedral and integrality constraints enables versatile modeling, but poses significant computational challenges. We investigate a method to address these problems based on sequential…

Most quasi-Monte Carlo research focuses on sampling from the unit cube. Many problems, especially in computer graphics, are defined via quadrature over the unit triangle. Quasi-Monte Carlo methods for the triangle have been developed by…

In this paper, we propose a Feasible Sequential Linear Programming (FSLP) algorithm applied to time-optimal control problems (TOCP) obtained through direct multiple shooting discretization. This method is motivated by TOCP with nonlinear…