Related papers: A geometric way to build strong mixed-integer prog…
We present a methodology for computing the flexibility index when uncertainty is characterized using multivariate Gaussian random variables. Our approach computes the flexibility index by solving a mixed-integer conic program (MICP). This…
Several different ways exist for approaching hard optimization problems. Mathematical programming techniques, including (integer) linear programming-based methods and metaheuristic approaches, are two highly successful streams for…
In this paper we propose a method that uses Lagrange multipliers and numerical algebraic geometry to find all critical points, and therefore globally solve, polynomial optimization problems. We design a polyhedral homotopy algorithm that…
Geometric programming (GP) provides a power tool for solving a variety of optimization problems. In the real world, many applications of geometric programming (GP) are engineering design problems in which some of the problem parameters are…
Any integral convex polytope $P$ in $\mathbb{R}^N$ provides a $N$-dimensional toric variety $X_P$ and an ample divisor $D_P$ on this variety. This paper gives an explicit construction of the algebraic geometric error-correcting code on…
Mixed-Integer Linear Programming (MILP) plays an important role across a range of scientific disciplines and within areas of strategic importance to society. The MILP problems, however, suffer from combinatorial complexity. Because of…
Mixed Integer Linear Programming (MILP) is a pillar of mathematical optimization that offers a powerful modeling language for a wide range of applications. During the past decades, enormous algorithmic progress has been made in solving…
We develop a method for solving elliptic partial differential equations on surfaces described by CAD patches that may have gaps/overlaps. The method is based on hybridization using a three-dimensional mesh that covers the gap/overlap…
A novel two-phase molecule inference framework, mol-infer, has recently been developed to infer chemical graphs with prescribed abstract structures and desired property values through mixed integer linear programming (MILP) under the…
In this paper, we present a novel method for solving multiobjective linear programming problems (MOLPP) that overcomes the need to calculate the optimal value of each objective function. This method is a follow-up to our previous work on…
Current state-of-the-art solvers for mixed-integer programming (MIP) problems are designed to perform well on a wide range of problems. However, for many real-world use cases, problem instances come from a narrow distribution. This has…
We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably…
A connected matching in a graph G consists of a set of pairwise disjoint edges whose covered vertices induce a connected subgraph of G. While finding a connected matching of maximum cardinality is a well-solved problem, it is NP-hard to…
For robots to successfully execute tasks assigned to them, they must be capable of planning the right sequence of actions. These actions must be both optimal with respect to a specified objective and satisfy whatever constraints exist in…
We propose a dual dynamic integer programming (DDIP) framework for solving multi-scale mixed-integer model predictive control (MPC) problems. Such problems arise in applications that involve long horizons and/or fine temporal…
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…
While Mixed-integer linear programming (MILP) is NP-hard in general, practical MILP has received roughly 100--fold speedup in the past twenty years. Still, many classes of MILPs quickly become unsolvable as their sizes increase, motivating…
This paper presents an efficient approach for the evaluation of multi-parametric mixed integer quadratic programming (mp-MIQP) solutions, occurring for instance in control problems involving discrete time hybrid systems with quadratic cost.…
Basis path testing is a cornerstone of structural testing, yet traditional automated methods, relying on greedy graph-traversal algorithms (e.g., DFS/BFS), often generate sub-optimal paths. This structural inferiority is not a trivial…
We propose a new exact approach for solving integer linear programming (ILP) problems which we will call projective splitting algorithms (PSAs). Unlike classical methods for solving ILP problems, PSAs conduct the search for the optimal…