25th International Symposium on Mathematical Programming (ISMP)

GAMS will attend the ISMP in Montréal!

We are happy to announce that our experienced colleagues will attend the conference and have a talk about our latest developments. We are looking forward to meet colleagues and other optimization enthusiasts.

GAMS has a speech on Monday, 22nd, at 14:00 - 16:00 — Parallel Sessions
Topic: Recent modeling language extensions: Stochastics and beyond

GAMSPy: Algebraic Modeling and Python

presented by
Steven Dirkse, GAMS Development Corporation
Muhammet Soytürk, GAMS Software Gmbh
Adam Christensen, GAMS Development Corporation

Optimization applications combine technology and expertise from many different areas, including model-building, algorithms, and data-handling. Often, the gathering, pre/post-processing, and visualization of the data is done by a diverse organization-spanning group that shares a common bond: their skill in and appreciation for Python and the vast array of available packages it provides. For this reason, GAMS offers a new comfortable way to integrate with Python on the data-handling and modeling side. In this talk, we will explore the benefits of our Python library GAMSPy.

For this year’s program, we would like to promote another talk as well presented by our Partner Olivier Huber:

DAG-based modeling framework for extended mathematical programming

presented by
Olivier Huber, University of Wisconsin Madison

We are investigating the modeling and design of algorithms for models with multiple optimization problems. This structure is present in many problem classes like bilevel/MPEC/multilevel programming or Nash equilibrium problems or whenever value functions present in the mappings of an optimization problem, like in multistage stochastic programming with coherent risk measures. Here, we tackle the challenge of modeling setups with any combination of the above structures. For instance, decentralized energy markets with part of the problem data being subjected to uncertainty can feature a Nash equilibrium problem where market participants have a nonsmooth objective function due to the presence of a coherent risk measure.

For such complex but structured setups, we propose a modeling framework based on a directed acyclic graph (DAG) structure. The nodes are of two types: the first one subsumes parametric optimization problems and variational inequalities, while the second one indicates a Nash behavior between its children nodes. Edges between two optimization problems specifies their interaction: either a hierarchical one (bilevel/MPEC) or the value function of the child appears in the parent problem.

This DAG structure is leveraged by model transformations to transform part or all of the problem in a form amenable to computation by existing solvers. When tackling some discrete stochastic programs, the reformulated problems do then belong to a classical model type and high-performance solvers for discrete optimization problem can be used to compute a solution. The DAG is also useful in the design of decomposition algorithms for solving complex instances. An implementation of these ideas is present in ReSHOP, a reformulation solver for hierarchical optimization problems.