SIAM Journal on Optimization, Volume 34, Issue 2, Page 1515-1539, June 2024. Abstract. The Fritz John (FJ) and Karush–Kuhn–Tucker (KKT) conditions are fundamental tools for characterizing minimizers and form the basis of almost all methods for constrained optimization. Since the seminal works of Fritz John, Karush, Kuhn, and Tucker, FJ/KKT conditions...

SIAM Journal on Optimization, Volume 34, Issue 2, Page 1490-1514, June 2024. Abstract. We study optimal simple second-order cone representations (a particular subclass of second-order cone representations) for weighted geometric means, which turns out to be closely related to minimum mediated sets. Several lower bounds and upper bounds on the size...

SIAM Journal on Optimization, Volume 34, Issue 2, Page 1455-1489, June 2024. Abstract. Recent years have seen significant advances in quantum/quantum-inspired technologies capable of approximately searching for the ground state of Ising spin Hamiltonians. The promise of leveraging such technologies to accelerate the solution of difficult optimization...

SIAM Journal on Optimization, Volume 34, Issue 2, Page 1402-1426, June 2024. Abstract. In this article, a family of SDEs are derived as a tool to understand the behavior of numerical optimization methods under random evaluations of the gradient. Our objective is to transpose the introduction of continuous versions through ODEs to understand the asymptotic...

SIAM Journal on Optimization, Volume 34, Issue 2, Page 1427-1454, June 2024. Abstract. Orthogonal group synchronization is the problem of estimating [math] elements [math] from the [math] orthogonal group given some relative measurements [math]. The least-squares formulation is nonconvex. To avoid its local minima, a Shor-type convex relaxation squares...

SIAM Journal on Optimization, Volume 34, Issue 2, Page 1374-1401, June 2024. Abstract. A popular approach to minimizing a finite sum of smooth convex functions is stochastic gradient descent (SGD) and its variants. Fundamental research questions associated with SGD include (i) how to find a lower bound on the number of times that the gradient oracle...