We consider the asymptotic distribution of the IP sparsity function, which measures the minimal support of optimal IP solutions, and the IP to LP distance function, which measures the distance between optimal IP and LP solutions. We create a framework for studying the asymptotic distribution of general functions related to integer optimization. There has been a significant amount of research focused around the extreme values that these functions can attain, however less is known about their typical values. Each of these functions is defined for a fixed constraint matrix and objective vector while the right hand sides are treated as input. We show that the typical values of these functions are smaller than the known worst case bounds by providing a spectrum of probability-like results that govern their overall asymptotic distributions.
A Comparison of the Embedding Method to Multi-Parametric Programming, Mixed-Integer Programming, Gradient-Descent, and Hybrid Minimum Principle Based Methods
Purdue University（普渡大学）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）
Fusing Backdoors, Machine Learning, and Optimization for Large-Scale Parametric Mixed-Integer Programs
Department of Operations and Decision Systems, Université Laval（Université Laval 运营与决策系统系）；H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology（Georgia Institute of Technology 工业与系统工程H. Milton Stewart学校）
Learning to Optimize for Mixed-Integer Non-linear Programming with Feasibility Guarantees
Department of Mechanical and Industrial Engineering（机械与工业工程系）；University of Toronto（多伦多大学）；Department of Civil and Systems Engineering（土木与系统工程系）；The Ralph O’Connor Sustainable Energy Institute (ROSEI)（拉尔夫·奥康纳可持续能源研究所）；Data Science and AI Institute (DSAI)（数据科学与人工智能研究所）；Johns Hopkins University（约翰霍普金斯大学）
