Algorithm-Hardware Co-Optimization of the Memristor-Based Framework for Solving SOCP and Homogeneous QCQP Problems

TL;DR

This paper introduces a memristor crossbar-based framework utilizing ADMM to solve SOCP and homogeneous QCQP problems with significantly reduced computational complexity, enabling faster and scalable convex optimization solutions.

Contribution

It presents the first memristor crossbar-based approach for convex optimization, achieving pseudo-O(N) complexity for solving SOCP and QCQP problems.

Findings

Achieves O(1) time for solving linear systems with memristor crossbar.

Reduces complexity from O(N^3.5-4) to pseudo-O(N).

Demonstrates potential for high-speed, scalable convex optimization hardware.

Abstract

A memristor crossbar, which is constructed with memristor devices, has the unique ability to change and memorize the state of each of its memristor elements. It also has other highly desirable features such as high density, low power operation and excellent scalability. Hence the memristor crossbar technology can potentially be utilized for developing low-complexity and high-scalability solution frameworks for solving a large class of convex optimization problems, which involve extensive matrix operations and have critical applications in multiple disciplines. This paper, as the first attempt towards this direction, proposes a novel memristor crossbar-based framework for solving two important convex optimization problems, i.e., second-order cone programming (SOCP) and homogeneous quadratically constrained quadratic programming (QCQP) problems. In this paper, the alternating direction method of multipliers (ADMM) is adopted. It splits the SOCP and homogeneous QCQP problems into sub-problems that involve the solution of linear systems, which could be effectively solved using the memristor crossbar in O(1) time complexity. The proposed algorithm is an iterative procedure that iterates a constant number of times. Therefore, algorithms to solve SOCP and homogeneous QCQP problems have pseudo-O(N) complexity, which is a significant reduction compared to the state-of-the-art software solvers (O(N^3.5) - O(N^4)).