CCosmo: A Custom First-Order Conic Solver
CCosmo is a custom conic solver family built around structure-aware linear algebra and batch solves.Motivation
Convex optimization appears throughout robotics, but in markedly different forms: small, dense quadratic programs (QPs) arise in online whole-body control, inverse-kinematics controllers, and reduced-order MPC controllers; moderately sized, sparse and dense quadratic and second-order cone programs (SOCPs) arise naturally in grasp selection and contact planning problems due to friction constraints; large, structured, and sparse problems arise in the context of trajectory optimization, with complicated semidefinite constraints becoming increasingly popular in the localization, perception, and motion planning communities.
In many of these applications, solvers are part of a larger planning, control, or estimation loop that repeatedly solve closely related problems to moderate accuracy at high speeds. This setting favors first-order methods, which have low memory requirements, are naturally warm started, and often converge rapidly to the accuracy required in the outer loop. Moreover, the relative simplicity of first-order methods makes them easy to customize to different classes of instances, sizes, and hardware such as massive programs on compute clusters, tiny programs on embedded hardware, or batches of programs on GPUs.
Contribution
CCosmo is a C++ implementation of a first-order conic optimization method designed to be customized around the problem family being solved. The core solver handles convex programs with quadratic costs.
CCosmo is based on the same algorithm as the popular OSQP and COSMO.jl solvers from the Oxford Control Group.
In addition to the usual quadratic-cost, convex standard form program, CCosmo supports programs in a matrix-standard-form that commonly arises when solving convex relaxations of non-convex programs. This is enabled by a custom matrix-linear-algebra backend.
Finally, CCosmo also includes a GPU backend for solving large batches of very small programs.
Results
PENDING CODE RELEASE
Code
CCosmo will be released publicly soon!
I am a final-year PhD candidate at MIT, advised by Pablo Parrilo and Russ Tedrake, working at the intersection of mathematical optimization, robotics, and reliable autonomy. My research develops scalable algorithms for high-performance decision-making, particularly in robotics.
I am interested in the entire decision-making pipeline, from high-level modeling, high-performance solver implementations, and low-level linear algebra to enable faster optimal decisions. I specialize in semidefinite programming and sums-of-squares optimization and development of convex optimization solvers. A central theme in my work is turning mathematical structure into computation. I build algorithms that exploit polynomial, conic, and graph structure to make difficult problems tractable, and am committed to distributing robust, open-source implementations of my methods.
I wrote CCosmo, a C++ first-order conic solver family, and VEGA, a decomposition solver for Graphs of Convex Sets. I am also an active contributor to Drake’s optimization, geometry, and planning stack. I am interested in industrial research roles where rigorous optimization, scalable algorithms, and high-quality software can push the frontier of AI, robotics, autonomy, and scientific computing.