Workshop on Mixed-Integer PDE-Constrained Optimization (MIPDECO)

Participation by invitation only.


This workshop will be held at SAMSI in RTP.


Many complex science and engineering applications can be formulated as optimization problems, constrained by Partial Differential Equations (PDEs), that involve both continuous and integer variables. This new class of problems, called mixed-integer PDE-constrained optimization (MIPDECO), must overcome the combinatorial challenge of integer decision variables combined with the numerical and computational complexity of PDE-constrained optimization. We briefly review the existing literature in terms of application and solution approaches to MIPDECO, and present a collection of test problems. Our preliminary numerical results highlight the tremendous challenges of this new class of problems.

MIPDECO have the potential to impact a broad range of science and engineering applications. For instance, the design of nuclear plants depends on selecting different types of core (fuel rod) configurations while controlling flow rates to maximize the heat extraction process. Remediation of contaminated sites and maximizing oil recovery both involve flow through porous media to determine the number of well-bores in addition to calculating optimal flow rates, and operational schedule. Related applications also arise in the optimal schedule of shale-gas recovery. Next-generation solar cells face complicated geometric and discrete design decisions to achieve perfect electromagnetic performance. In disaster-recovery scenarios, such as oil spills, wildfires, and hurricanes, resources need to be scheduled for mitigation purposes while predicting material properties to calibrate the underlying dynamics for accurate forecasts. Many other science and engineering examples have similar decision-making characteristics including wind farm design, climate science, and the design, control, and operation of gas networks. The common theme of these applications is a need to address integral and continuous optimization variables in the context of large-scale multi-physics applications.

Schedule and Supporting Media

Printable Schedule

Planning for this event is ongoing. Updates will be posted to this page as they transpire.

Wednesday, March 29, 2017
SAMSI, Room 150

Description Speaker Slides Videos
Welcome and Introduction Richard Smith, SAMSI Director
“Introduction to Shape Optimization” Volker Schulz, Universität Trier (GER)
“Introduction to Mixed-Integer Optimization” Sven Leyffer, Argonne National Laboratory

Thursday, March 30, 2017
SAMSI, Room 150

Description Speaker Slides Videos
Working Groups
Working Groups (continued)
GROUP REPORTS (three short presentations from each group)
“Methods for PDE Constrained Optimization” Bart van Bloemen-Waanders, Sandia National Laboratories
“Tutorial – PDE Constrained Optimization with Julia” Lars Ruthotto, Emory University
“Exploiting Problem Structure in Mixed-Integer PDE-Constrained Optimization” Joey Hart, N.C. State University

Friday, March 31, 2017
SAMSI, Room 150

Description Speaker Slides Videos
BRAINSTORMING -Planning next steps
Paper Writing in Groups
Paper Writing in Groups (continued)
Working Groups and Wrap Up – Final discussions and tasks

Questions: email [email protected]