# Optimization of random cost functions and statistical physics

arxiv（2024）

Abstract

This is the text of my report presented at the 29th Solvay Conference on
Physics on `The Structure and Dynamics of Disordered Systems' held in Bruxelles
from October 19 to 21, 2023. I consider the problem of minimizing a random
energy function H(σ), where σ is an N-dimensional vector, in
the high-dimensional regime N≫ 1. Using as a reference point a 1986 paper
by Fu and Anderson, I take stock of the progress on this question over the last
40 years. In particular, I focus on the influence and ramifications of ideas
originating from statistical physics. My own conclusion is that several of the
most fundamental questions in this area (which in 1986 were barely formulated)
have now received mathematically rigorous answers, at least in simple – yet
highly nontrivial – settings. Instrumental to this spectacular progress was
the dialogue between different research communities: physics, computer science,
mathematics.

MoreTranslated text

AI Read Science

Must-Reading Tree

Example

Generate MRT to find the research sequence of this paper

Chat Paper

Summary is being generated by the instructions you defined