Take Action

Home | Faculty & Research Overview | Research

Research Details

Tractable stochastic analysis in high dimensions via robust optimization, Mathematical Programming


Modern probability theory, whose foundation is based on the axioms set forth by Kolmogorov, is currently the major tool for performance analysis in stochastic systems. While it offers insights in understanding such systems, probability theory, in contrast to optimization, has not been developed with computational tractability as an objective when the dimension increases. Correspondingly, some of its major areas of application remain unsolved when the underlying systems become multidimensional: Queueing networks, auction design in multi-item, multi-bidder auctions, network information theory, pricing multi-dimensional options, among others. We propose a new approach to analyze stochastic systems based on robust optimization. The key idea is to replace the Kolmogorov axioms and the concept of random variables as primitives of probability theory, with uncertainty sets that are derived from some of the asymptotic implications of probability theory like the central limit theorem. In addition, we observe that several desired system properties such as incentive compatibility and individual rationality in auction design are naturally expressed in the language of robust optimization. In this way, the performance analysis questions become highly structured optimization problems (linear, semidefinite, mixed integer) for which there exist efficient, practical algorithms that are capable of solving problems in high dimensions. We demonstrate that the proposed approach achieves computationally tractable methods for (a) analyzing queueing networks, (b) designing multi-item, multi-bidder auctions with budget constraints, and (c) pricing multi-dimensional options.




Chaithanya Bandi, Dimitris Bertsimas

Date Published



Bandi, Chaithanya, and Dimitris Bertsimas. 2012. Tractable stochastic analysis in high dimensions via robust optimization. Mathematical Programming. 134(1): 23-70.


Explore leading research and ideas

Find articles, podcast episodes, and videos that spark ideas in lifelong learners, and inspire those looking to advance in their careers.
learn more


Review Courses & Schedules

Access information about specific courses and their schedules by viewing the interactive course scheduler tool.


Discover the path to your goals

Whether you choose our Full-Time, Part-Time or Executive MBA program, you’ll enjoy the same unparalleled education, exceptional faculty and distinctive culture.
learn more

Take Action