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A Technical Note on the Implementation and Use of PDCS

Zhenwei Lin, Zikai Xiong, Dongdong Ge, Yinyu Ye

Abstract

This technical note documents the implementation and use of the Primal-Dual Conic Programming Solver (PDCS), a first-order solver for large-scale conic optimization problems introduced by Lin et al. (arXiv:2505.00311). It describes the algorithmic and implementation details underlying PDCS, including the restarted primal-dual hybrid gradient method framework, adaptive step-size selection, adaptive reflected Halpern iterations, adaptive restarts, and diagonal preconditioning. It also provides practical instructions for using PDCS, including its interfaces with JuMP and CVXPY, solver options, and illustrative code examples. PDCS is available at https://github.com/ZikaiXiong/PDCS under the Apache License 2.0.

A Technical Note on the Implementation and Use of PDCS

Abstract

This technical note documents the implementation and use of the Primal-Dual Conic Programming Solver (PDCS), a first-order solver for large-scale conic optimization problems introduced by Lin et al. (arXiv:2505.00311). It describes the algorithmic and implementation details underlying PDCS, including the restarted primal-dual hybrid gradient method framework, adaptive step-size selection, adaptive reflected Halpern iterations, adaptive restarts, and diagonal preconditioning. It also provides practical instructions for using PDCS, including its interfaces with JuMP and CVXPY, solver options, and illustrative code examples. PDCS is available at https://github.com/ZikaiXiong/PDCS under the Apache License 2.0.
Paper Structure (16 sections, 18 equations, 1 table, 4 algorithms)

This paper contains 16 sections, 18 equations, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries on Conic Optimization and PDHG
  3. PDHG for conic programs
  4. Algorithmic enhancements in PDCS
  5. Adaptive step size
  6. Adaptive reflected Halpern iteration
  7. Adaptive restart
  8. Computation of the normalized duality gap
  9. Primal weight adjustment
  10. Diagonal rescaling and projections onto rescaled cones
  11. Installation and use of PDCS
  12. Installation
  13. Usage
  14. JuMP Interface
  15. CVXPY Interface
  16. ...and 1 more sections

Theorems & Definitions (1)

  • Definition 2.1: normalized duality gap xiong2024role