Exceptional Operations Research
The journal Mathematics of Operations Research (MOR) is a foremost academic journal published quarterly by the Institute for Operations Research and the Management Sciences (INFORMS), a leading professional organization for decision and data sciences. The core focus for the journal Mathematics of Operations Research lies in Continuous Optimization, Discrete Optimization, Stochastic Models, and Game Theory. Its current Editor-in-Chief is Jose Blanchet, a professor at Stanford University. The journal was founded in 1976 and is celebrating its 50th year. To celebrate this milestone, the Editor-in-Chief has assembled a list of 50 papers, one for each year, published in the journal and exemplary in more than one way. We're proud to find a quick perusal of the list reveals some of our colleagues here at the UC Davis Department of Mathematics.
The paper chosen for the year 2006 is Integer Polynomial Optimization in Fixed Dimension, by our Department members De Loera and Koeppe, as well as co-authors Hemmecke (a VRAP in our Department around that time) and Weismantel. This work looks at different integer optimization problems and groups them based on how difficult they are to solve. It focuses on cases where the equations and objectives are polynomial functions with integer coefficients, and the number of variables stays fixed. The authors present an algorithm that can find upper and lower estimates for the best possible solution when optimizing a polynomial over integer points inside a convex shape. For polynomials that are always nonnegative in that region, these estimates can be refined into an efficient approximation method that can get very close to the optimal solution in polynomial time.
Also worth noting is the paper chosen to represent 1991: Scenarios and Policy Aggregation in Optimization Under Uncertainty, by our late colleague Wets and co-author Rockafellar. When dealing with long-term planning problems where there's a lot of uncertainty and not enough reliable data for traditional probability-based models, a common strategy is to create and analyze several possible future scenarios. The goal is to find patterns that help build decisions that work well across different situations. This paper introduces a systematic method for creating those robust decision strategies. It groups scenarios based on what information is available at different stages and gradually adjusts decisions so they rely only on information that would realistically be known at the time, rather than benefiting from hindsight.
We congratulate our colleagues for being recognized as exemplary authors!