Related papers: Optimization and Sampling Under Continuous Symmetr…
The uniform sampling of convex polytopes is an interesting computational problem with many applications in inference from linear constraints, but the performances of sampling algorithms can be affected by ill-conditioning. This is the case…
We systematically explore a class of constrained optimization problems with linear objective function and constraints that are linear combinations of logarithms of the optimization variables. Such problems can be viewed as a generalization…
We introduce a class of stochastic algorithms for minimizing weakly convex functions over proximally smooth sets. As their main building blocks, the algorithms use simplified models of the objective function and the constraint set, along…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
We develop a new unsupervised symmetry learning method that starts with raw data and provides the minimal generator of an underlying Lie group of symmetries, together with a symmetry-equivariant representation of the data, which turns the…
We consider convex programming problems with integrality constraints that are invariant under a linear symmetry group. To decompose such problems we introduce the new concept of core points, i.e., integral points whose orbit polytopes are…
We study distributed composite optimization over networks: agents minimize the sum of a smooth (strongly) convex function, the agents' sum-utility, plus a non-smooth (extended-valued) convex one. We propose a general algorithmic framework…
Optimization problems arising in data science have given rise to a number of new derivative-based optimization methods. Such methods often use standard smoothness assumptions -- namely, global Lipschitz continuity of the gradient function…
In probability theory and statistics, the IID model represents a single population, and a large, potentially infinite sample from this population. Main theorems, in particular the central limit theorem and laws of large number (LLN) assure…
We develop randomized (block) coordinate descent (CD) methods for linearly constrained convex optimization. Unlike most CD methods, we do not assume the constraints to be separable, but let them be coupled linearly. To our knowledge, ours…
Sampling biases in training data are a major source of algorithmic biases in machine learning systems. Although there are many methods that attempt to mitigate such algorithmic biases during training, the most direct and obvious way is…
Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical…
This research studies a non-convex geometric optimization problem arising from the field of optical wireless power transfer. In the considered optimization problem, the cost function is a sum of negatively and fractionally powered distances…
Group-invariant probability distributions appear in many data-generative models in machine learning, such as graphs, point clouds, and images. In practice, one often needs to estimate divergences between such distributions. In this work, we…
We study stochastic convex optimization under infinite noise variance. Specifically, when the stochastic gradient is unbiased and has uniformly bounded $(1+\kappa)$-th moment, for some $\kappa \in (0,1]$, we quantify the convergence rate of…
Gradient descent methods and especially their stochastic variants have become highly popular in the last decade due to their efficiency on big data optimization problems. In this thesis we present the development of data sampling strategies…
This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…
This paper provides examples of various synchronous and asynchronous signal processing systems for performing optimization, utilizing the framework and elements developed in a preceding paper. The general strategy in that paper was to…
An algorithm for solving nonconvex smooth optimization problems is proposed, analyzed, and tested. The algorithm is an extension of the Trust Region Algorithm with Contractions and Expansions (TRACE) [Math. Prog. 162(1):132, 2017]. In…
We present complexity and numerical results for a new asynchronous parallel algorithmic method for the minimization of the sum of a smooth nonconvex function and a convex nonsmooth regularizer, subject to both convex and nonconvex…