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A memristor crossbar, which is constructed with memristor devices, has theunique ability to change and memorize the state of each of its memristorelements. It also has other highly desirable features such as high density, lowpower operation and excellent scalability. Hence the memristor crossbartechnology can potentially be utilized for developing low-complexity andhigh-scalability solution frameworks for solving a large class of convexoptimization problems, which involve extensive matrix operations and havecritical applications in multiple disciplines. This paper, as the first attempttowards this direction, proposes a novel memristor crossbar-based framework forsolving two important convex optimization problems, i.e., second-order coneprogramming (SOCP) and homogeneous quadratically constrained quadraticprogramming (QCQP) problems. In this paper, the alternating direction method ofmultipliers (ADMM) is adopted. It splits the SOCP and homogeneous QCQP problemsinto sub-problems that involve the solution of linear systems, which could beeffectively solved using the memristor crossbar in O(1) time complexity. Theproposed algorithm is an iterative procedure that iterates a constant number oftimes. Therefore, algorithms to solve SOCP and homogeneous QCQP problems havepseudo-O(N) complexity, which is a significant reduction compared to thestate-of-the-art software solvers (O(N^3.5) - O(N^4)).

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