math.OC · 2026-08-18 · No. 88

Optimization and Control, 2026-08-18.

2 new papers in math.OC. Titles, authors, abstracts. Links to arXiv. Want this in your inbox every morning? Subscribe →

01 — The papers

2 entries
  1. 01

    A Two-Stage Learning PINN Approach for Solving the Inverse Problem of the 1D Porous Medium Equation

    Noura Al Helwani, Sophie Moufawad, Nabil Nassif

    math.OC · cs.AI

    The Porous Medium Equation (PME), given by $u_t = Δ(u^m)$ for $m > 1$, is a degenerate nonlinear parabolic partial differential equation that arises in various physical applications such as fluid flow in porous media, heat transfer in plasmas, and population dynamics. It is known for its nonlinear diffusion and finite propagation speed. In this paper, we study numerical solutions of the one-dimensional direct and inverse PME using...

    arxiv.org/abs/2608.16475 · PDF

  2. 02

    Stochastic Gradient Tracking over Time-Varying Networks: One-Step Lyapunov Analysis

    Sulaiman A. Alghunaim

    math.OC · cs.DC · eess.SY

    We study decentralized stochastic gradient tracking over a time-varying network of $N$ agents under a uniform window-mixing condition. Products of $τ$ consecutive doubly stochastic mixing matrices contract disagreement by a factor $λ<1$, although individual matrices need not contract disagreement strictly and individual communication graphs may be disconnected. We construct a time-varying quadratic norm that turns this window contraction into...

    arxiv.org/abs/2608.16271 · PDF

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