arXiv subjects

Govind M. Chari

Publications and source records attributed to Govind M. Chari.

6 recordsLinked to original sources

arXiv2026

Optimal Acceleration for Proximal Minimization of the Sum of Convex and Strongly Convex Functions

When minimizing the sum of a convex and a strongly convex function, or when finding the zero of the sum of a monotone operator and a strongly monotone operator, Chambolle and Pock (2010) and Davis and Yin (2015) proposed accelerated mechanisms that achieve an $\mathcal{O}(1/N^2)$ convergence rate for the squared distance to the solution, but the optimality of this rate was not established. In this work, we present Fast Douglas--Rachford Splitting (FDR), an accelerated method that improves the constants established in the prior works, and provide a complexity lower bound establishing that both the $\mathcal{O}(1/N^2)$ convergence rate and the leading-order constant of FDR's rate are optimal.

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arXiv2026

QOCO-GPU: A Quadratic Objective Conic Optimizer with GPU Acceleration

We present a GPU-accelerated backend for QOCO, a C-based solver for quadratic objective second-order cone programs (SOCPs) based on a primal-dual interior point method. Our backend uses NVIDIA's cuDSS library to perform a direct sparse LDL factorization of the KKT system at each iteration. We also develop custom CUDA kernels for cone operations and show that parallelizing these operations is essential for achieving peak performance. Additionally, we refactor QOCO to introduce a modular backend abstraction that decouples solver logic from the underlying linear algebra implementations, allowing the existing CPU and new GPU backend to share a unified codebase. This GPU backend is accessible through a direct Python interface and through CVXPY, allowing for easy use. Numerical experiments on a range of large-scale quadratic programs and SOCPs with tens to hundreds of millions of nonzero elements in the KKT matrix, demonstrate speedups of up to 50-70 times over the CPU implementation.

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arXiv2024

Constraint Preconditioning and Parameter Selection for a First-Order Primal-Dual Method applied to Model Predictive Control

Many techniques for real-time trajectory optimization and control require the solution of optimization problems at high frequencies. However, ill-conditioning in the optimization problem can significantly reduce the speed of first-order primal-dual optimization algorithms. We introduce a preconditioning technique and step-size heuristic for Proportional-Integral Projected Gradient (PIPG), a first-order primal-dual algorithm. The preconditioning technique, based on the QR factorization, aims to reduce the condition number of the KKT matrix associated with the optimization problem. Our step-size selection heuristic chooses step-sizes to minimize the upper bound on the convergence of the primal-dual gap for the optimization problem. These algorithms are tested on two model predictive control problem examples and show a solve-time reduction of at least 3.6x.

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arXiv2024

Fast Monte Carlo Analysis for 6-DoF Powered-Descent Guidance via GPU-Accelerated Sequential Convex Programming

We introduce a GPU-accelerated Monte Carlo framework for nonconvex, free-final-time trajectory optimization problems. This framework makes use of the prox-linear method, which belongs to the larger family of sequential convex programming (SCP) algorithms, in conjunction with a constraint reformulation that guarantees inter-sample constraint satisfaction. Key features of this framework are: (1) continuous-time constraint satisfaction; (2) a matrix-inverse-free solution method; (3) the use of the proportional-integral projected gradient (PIPG) method, a first-order convex optimization solver, customized to the convex subproblem at hand; and, (4) an end-to-end, library-free implementation of the algorithm. We demonstrate this GPU-based framework on the 6-DoF powered-descent guidance problem, and show that it is faster than an equivalent serial CPU implementation for Monte Carlo simulations with over 1000 runs. To the best of our knowledge, this is the first GPU-based implementation of a general-purpose nonconvex trajectory optimization solver.

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arXiv2024

Spacecraft Rendezvous Guidance via Factorization-Free Sequential Convex Programming using a First-Order Method

We implement a fully factorization-free algorithm for nonconvex, free-final-time trajectory optimization. This algorithm is based on sequential convex programming and utilizes an inverse-free, exact discretization procedure to ensure dynamic feasibility of the converged trajectory and PIPG, a fast, first-order conic optimization algorithm as the subproblem solver. Although PIPG requires the tuning of a hyperparameter to achieve fastest convergence, we show that PIPG can be tuned to a nominal trajectory optimization problem and it is robust to variations in initial condition. We demonstrate this with a monte carlo simulation of the free-final-time rendezvous problem, using Clohessy-Wiltshire dynamics, an impulsive thrust model, and various state and control constraints including a spherical keepout zone.

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arXiv2023

Real-Time Sequential Conic Optimization for Multi-Phase Rocket Landing Guidance

We introduce a multi-phase rocket landing guidance framework that can handle nonlinear dynamics and does not mandate any additional mixed-integer or nonconvex constraints to handle discrete temporal events/switching. To achieve this, we first introduce sequential conic optimization (SeCO), a new paradigm for solving nonconvex optimal control problems that is entirely devoid of matrix factorizations and inversions. This framework combines sequential convex programming (SCP) and first-order conic optimization and can solve unified multi-phase trajectory optimization problems in real-time. The novel features of this framework are: (1) time-interval dilation, which enables multi-phase trajectory optimization with free-transition-time; (2) single-crossing compound state-triggered constraints, which are entirely convex if the trigger and constraint conditions are convex; (3) virtual state, which is a new approach to handling artificial infeasibility in SCP methods that preserves the shapes of the constraint sets; and, (4) the use of the proportional-integral projected gradient method (PIPG), a high-performance first-order conic optimization solver, in tandem with the penalized trust region (PTR) SCP algorithm. We demonstrate the efficacy and real-time capability of SeCO by solving a relevant multi-phase rocket landing guidance problem with nonlinear dynamics and convex constraints only, and observe that our solver is 2.7 times faster than a state-of-the-art convex optimization solver.

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