arXiv subjects

Toshiaki Yamanaka

Publications and source records attributed to Toshiaki Yamanaka.

2 recordsLinked to original sources

arXiv2025

TSP integrality gap via 2-edge-connected multisubgraph problem under coincident IP optima

Determining the integrality gap of the linear programming (LP) relaxation of the metric traveling salesman problem (TSP) remains a long-standing open problem. We introduce a transfer principle: when the integer optimum of the 2-edge-connected multisubgraph problem (2ECM) is a unique Hamiltonian cycle $T$, any $α$-approximation algorithm for 2ECM that outputs a Hamiltonian cycle yields an $α$-approximation for TSP. We further develop a cut-margin stability framework that certifies $T$ as the unique integer optimum for both problems and is stable under $\ell_\infty$-bounded perturbations. We show that, if instances exist where the 2ECM has both a unique Hamiltonian cycle integer optimum and a half-integral LP solution, then the TSP integrality gap is at most 4/3 by the algorithm of Boyd et al. (SIAM Journal on Discrete Mathematics 36:1730--1747, 2022). Constructing such instances remains an open problem.

math.OC↗

arXiv2025

Coordinated Mean-Field Control for Systemic Risk

We develop a robust linear-quadratic mean-field control framework for systemic risk under model uncertainty, in which a central bank jointly optimizes interest rate policy and supervisory monitoring intensity against adversarial distortions. Our model features multiple policy instruments with interactive dynamics, implemented via a variance weight that depends on the policy rate, generating coupling effects absent in single-instrument models. We establish viscosity solutions for the associated HJB--Isaacs equation, prove uniqueness via comparison principles, and provide verification theorems. The linear-quadratic structure yields explicit feedback controls derived from a coupled Riccati system, preserving analytical tractability despite adversarial uncertainty. Simulations reveal distinct loss-of-control regimes driven by robustness-breakdown and control saturation, alongside a pronounced asymmetry in sensitivity between the mean and variance channels. These findings demonstrate the importance of instrument complementarity in systemic risk modeling and control.

math.OC↗