2 research outputs found
Algorithm-Hardware Co-Optimization of the Memristor-Based Framework for Solving SOCP and Homogeneous QCQP Problems
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))
A Memristor-Based Optimization Framework for AI Applications
Memristors have recently received significant attention as ubiquitous
device-level components for building a novel generation of computing systems.
These devices have many promising features, such as non-volatility, low power
consumption, high density, and excellent scalability. The ability to control
and modify biasing voltages at the two terminals of memristors make them
promising candidates to perform matrix-vector multiplications and solve systems
of linear equations. In this article, we discuss how networks of memristors
arranged in crossbar arrays can be used for efficiently solving optimization
and machine learning problems. We introduce a new memristor-based optimization
framework that combines the computational merit of memristor crossbars with the
advantages of an operator splitting method, alternating direction method of
multipliers (ADMM). Here, ADMM helps in splitting a complex optimization
problem into subproblems that involve the solution of systems of linear
equations. The capability of this framework is shown by applying it to linear
programming, quadratic programming, and sparse optimization. In addition to
ADMM, implementation of a customized power iteration (PI) method for
eigenvalue/eigenvector computation using memristor crossbars is discussed. The
memristor-based PI method can further be applied to principal component
analysis (PCA). The use of memristor crossbars yields a significant speed-up in
computation, and thus, we believe, has the potential to advance optimization
and machine learning research in artificial intelligence (AI)