primal-dual methods

Log-Averaged Mirror Prox for Fast, Large-Scale Optimal Transport in Linear Space

  • Matthew X. Burns
  • Jiaming Liang
    • Categories Convex Optimization, Parallel Algorithms Tags , , , ,

    We propose Log-Averaged Mirror Prox (LAMP), a linear-space primal-dual method for large-scale optimal transport. LAMP implements primal mirror prox updates by tracking an averaged dual sequence, reducing storage complexity from \({O}(nm)\) to \({O}(n+m)\) while preserving dense, GPU-friendly reductions. Consequently, LAMP preserves the last-iterate \(\widetilde{{O}}( nm\varepsilon^{-1})\) arithmetic complexity of conservatively parameterized primal-dual mirror prox. We further … Read more

    Policy with guaranteed risk-adjusted performance for multistage stochastic linear problems

  • Bernardo Freitas Paulo da Costa
  • Vincent Leclère
    • Categories Convex Optimization, Dynamic Programming, Stochastic Programming Tags , , ,

    Risk-averse multi-stage problems and their applications are gaining interest in various fields of applications. Under convexity assumptions, the resolution of these problems can be done with trajectory following dynamic programming algorithms like Stochastic Dual Dynamic Programming (SDDP) to access a deterministic lower bound, and dual SDDP for deterministic upper bounds. In this paper, we leverage … Read more