[MS Thesis Talk] Marble: An On-Manifold Approach to Solving Mathematical Programs with Complementarity Constraints

Date: Thursday, July 30, 2026 Time: 3:30 PM - 4:30 PM Location / ZOOM Link: (GHC 6115 / https://cmu.zoom.us/j/96096959582 ) Abstract: Many problems in robotics require reasoning over a mix of continuous dynamics and discrete events, such as making and breaking contact in manipulation and locomotion. These problems are locally well modeled by quadratic programs with complementarity constraints (QPCCs). While very expressive, QPCCs are non-convex problems, and few solvers exist for computing fast, local solutions for use in planning pipelines. In this work, we develop an open-source solver, Marble, designed to solve QPCCs using an on-manifold complementarity relaxation and homotopy technique. The resulting solver avoids many of the classical issues with complementarity constraints and exhibits competitive speed and robustness across QPCC benchmarks and robotics-specific examples compared to existing baselines. Committee: Zac Manchester (advisor) Rajan Gill Arun Bishop -- MICAH REICH MSR Student, Robotics Institute - CMU