We show how we can linearize probabilistic linear constraints with binary variables when all coefficients are distributed according to either N (μi, λμi), for some λ > 0 and μi > 0, or Γ(ki, θ) for some θ > 0 and ki > 0. The constraint can also be linearized when the coefficients are independent and identically distributed if they are, besides, either positive or strictly stable random variables.

In a Hierarchical Model Predictive Control (H-MPC) framework, this paper explores suitable time-variant structures for the hierarchies of different local MPC controllers. The idea is to adapt to different operational conditions by changing the importance of the local controllers. This is done by defining the level of the hierarchy they belong to, and solving within each level the local MPC prob...

Combinatorial auctions have recently attracted the interests of many researchers due to their promising applications such as the spectrum auctions recently held by the FCC. In a combinatorial auction, multiple items with interdependent values are sold simultaneously and bidders are allowed to bid on any combination of items. This paper presents a method for implementing several secure combinato...

This report is a brief exposition of some of the important links between machine learning and combinatorial optimization. We explain how efficient ‘learnability’ in standard probabilistic models of learning is linked to the existence of efficient randomized algorithms for certain natural combinatorial optimization problems, and we discuss the complexity of some of these optimization problems.

The traveling salesman problem (TSP) is the problem of finding the shortest tour through all the nodes that a salesman has to visit. The TSP is probably the most famous and extensively studied problem in the field of combinatorial optimization. Because this problem is an NP-hard problem, practical large-scale instances cannot be solved by exact algorithms within acceptable computational times. ...