The problem of packing ellipsoids in the n-dimensional space is considered in the present work. The proposed approach combines heuristic techniques with the resolution of recently introduced nonlinear programming models in order to construct solutions with a large number of ellipsoids. Numerical experiments illustrate that the introduced approach delivers good quality solutions with a computational … Read more
The alternating direction method of multipliers (ADMM) is being widely used in a variety of areas; its different variants tailored for different application scenarios have also been deeply researched in the literature. Among them, the linearized ADMM has received particularly wide attention from many areas because of its efficiency and easy implementation. To theoretically guarantee … Read more
Perspective functions have long been used to convert fractional programs into convex programs. More recently, they have been used to form tight relaxations of mixed-integer nonlinear programs with so-called indicator variables. Motivated by a practical application (maximising energy efficiency in an OFDMA system), we consider problems that have a fractional objective and indicator variables simultaneously. … Read more
The effect of preconditioning linear weighted least-squares using an approximation of the model matrix is analyzed, showing the interplay of the eigenstructures of both the model and weighting matrices. A small example is given illustrating the resulting potential inefficiency of such preconditioners. Consequences of these results in the context of the weakly-constrained 4D-Var data assimilation … Read more
We study in this paper min max robust combinatorial optimization problems for an uncertainty polytope that is defined by knapsack constraints, either in the space of the optimization variables or in an extended space. We provide exact and approximation algorithms that extend the iterative algorithms proposed by Bertismas and Sim (2003). We also study the … Read more
Recently, the generalized alternating direction method of multipliers (GADMM) proposed by Eckstein and Bertsekas has received wide attention, especially with respect to numerous applications. In this paper, we develop a new linearized version of generalized alternating direction method of multipliers (L-GADMM) for the linearly constrained separable convex programming whose objective functions are the sum of … Read more
In this paper, we propose new constraint generation algorithms for solving the two-stage robust minimum cost flow problem, a problem that arises from various applications such as transportation and logistics. In order to develop efficient algorithms under general polyhedral uncertainty set, we repeatedly exploit the network-flow structure to reformulate the two-stage robust minimum cost flow … Read more
We consider a novel method entitled constraints reduction programming which aims to reduce the constraints in an optimization model. This method is derived from various applications of management or decision making, and has potential ability to handle a wider range of applications. Due to the high combinatorial complexity of underlying model, it is difficult to … Read more
In this work, we study the problem of scheduling courses and instructors in the Mathematics Department at the United States Naval Academy (USNA) in a resilient manner. Every semester, the department needs to schedule around 70 instructors and 150-180 course sections into 30 class periods and 30 rooms. We formulate a stochastic integer linear program … Read more
Despite recent interest in multiobjective integer programming, few algorithms exist for solving biobjective mixed integer programs. We present such an algorithm: the Boxed Line Method. For one of its variants, we prove that the number of single-objective integer programs solved is bounded by a linear function of the number of nondominated line segments in the … Read more