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We introduce and study conic geometric programs (CGPs), which are convex optimization problems that unify geometric programs (GPs) and conic optimization problems such as semidefinite programs (SDPs). A CGP consists of a linear objective…
Symmetric positive definite (SPD) matrices are useful for capturing second-order statistics of visual data. To compare two SPD matrices, several measures are available, such as the affine-invariant Riemannian metric, Jeffreys divergence,…
Differential Privacy (DP) is becoming central to large-scale training as privacy regulations tighten. We revisit how DP noise interacts with adaptivity in optimization through the lens of stochastic differential equations, providing the…
Massive MIMO is currently a leading physical layer technology candidate that can dramatically enhance throughput in 5G systems, for both unicast and multicast transmission modalities. As antenna elements are becoming smaller and cheaper in…
Reconstruction of images from noisy linear measurements is a core problem in image processing, for which convex optimization methods based on total variation (TV) minimization have been the long-standing state-of-the-art. We present an…
Difference of Convex (DC) optimization problems have objective functions that are differences between two convex functions. Representative ways of solving these problems are the proximal DC algorithms, which require that the convex part of…
Large-scale constrained optimization problems are at the core of many tasks in control, signal processing, and machine learning. Notably, problems with functional constraints arise when, beyond a performance{\nobreakdash-}centric goal…
Stochastic gradient method (SGM) has been popularly applied to solve optimization problems with objective that is stochastic or an average of many functions. Most existing works on SGMs assume that the underlying problem is unconstrained or…
Numerical simulations of fluids in astrophysics and computational fluid dynamics (CFD) are among the most computationally-demanding calculations, in terms of sustained floating-point operations per second, or FLOP/s. It is expected that…
The learning objective plays a fundamental role to build a recommender system. Most methods routinely adopt either pointwise or pairwise loss to train the model parameters, while rarely pay attention to softmax loss due to its computational…
Tenfold improvements in computation speed can be brought to the alternating direction method of multipliers (ADMM) for Semidefinite Programming with virtually no decrease in robustness and provable convergence simply by projecting…
Random projection (RP) is a classical technique for reducing storage and computational costs. We analyze RP-based approximations of convex programs, in which the original optimization problem is approximated by the solution of a…
We address the problem of computing stationary points for non-smooth, non-convex optimization problems. While this topic is well studied in the smooth setting, fewer algorithmic and theoretical results exist for the non-smooth case. Within…
We extend recent computer-assisted design and analysis techniques for first-order optimization over structured functions--known as performance estimation--to apply to structured sets. We prove "interpolation theorems" for smooth and…
We propose a decomposition framework for the parallel optimization of the sum of a differentiable function and a (block) separable nonsmooth, convex one. The latter term is typically used to enforce structure in the solution as, for…
The robust truss topology optimization against the uncertain static external load can be formulated as mixed-integer semidefinite programming. Although a global optimal solution can be computed with a branch-and-bound method, it is very…
This paper proposes a general fixture layout design framework that directly integrates the system equation with the convex relaxation method. Note that the optimal fixture design problem is a large-scale combinatorial optimization problem,…
Data encoded as symmetric positive definite (SPD) matrices frequently arise in many areas of computer vision and machine learning. While these matrices form an open subset of the Euclidean space of symmetric matrices, viewing them through…
In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems.…
With today's increasing demand for digital devices in Substation Automation Systems (SAS) based on the IEC61850 standard, the measured data error due to the synchronization problem should be considered as a significant problem in…