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We present a variant of accelerated gradient descent algorithms, adapted from Nesterov's optimal first-order methods, for weakly-quasi-convex and weakly-quasi-strongly-convex functions. We show that by tweaking the so-called estimate…
We consider minimization of a smooth nonconvex function with inexact oracle access to gradient and Hessian (without assuming access to the function value) to achieve approximate second-order optimality. A novel feature of our method is that…
This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…
Recent theoretical developments in coset coding theory have provided continuous-valued functions which give the equivocation and maximum likelihood (ML) decoding probability of coset secrecy codes. In this work, we develop a method for…
We investigate a number of recently reported exact algorithms for the maximum clique problem (MCQ, MCR, MCS, BBMC). The program code used is presented and critiqued showing how small changes in implementation can have a drastic effect on…
Variational quantum algorithms rely on the optimization of parameterized quantum circuits in noisy settings. The commonly used back-propagation procedure in classical machine learning is not directly applicable in this setting due to the…
Difference of convex (DC) functions cover a broad family of non-convex and possibly non-smooth and non-differentiable functions, and have wide applications in machine learning and statistics. Although deterministic algorithms for DC…
Asynchronous-parallel algorithms have the potential to vastly speed up algorithms by eliminating costly synchronization. However, our understanding to these algorithms is limited because the current convergence of asynchronous (block)…
We study alternating first-order algorithms with no inner loops for solving nonconvex-strongly-concave min-max problems. We show the convergence of the alternating gradient descent--ascent algorithm method by proposing a substantially…
We seek tight bounds on the viable parallelism in asynchronous implementations of coordinate descent that achieves linear speedup. We focus on asynchronous coordinate descent (ACD) algorithms on convex functions which consist of the sum of…
An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…
We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…
We consider minimizing nonsmooth convex functions with bounded subgradients. However, instead of directly observing a subgradient at every step $k\in [0, \dots, N-1]$, we assume that the optimizer receives an adversarially corrupted…
The regret bound of an optimization algorithms is one of the basic criteria for evaluating the performance of the given algorithm. By inspecting the differences between the regret bounds of traditional algorithms and adaptive one, we…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
In this paper we present tight lower-bounds and new upper-bounds for hypergraph and database problems. We give tight lower-bounds for finding minimum hypercycles. We give tight lower-bounds for a substantial regime of unweighted hypercycle.…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
In this paper, we develop two new randomized block-coordinate optimistic gradient algorithms to approximate a solution of nonlinear equations in large-scale settings, which are called root-finding problems. Our first algorithm is…
In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a…
We consider minimizing an objective function subject to constraints defined by the intersection of lower-level sets of convex functions. We study two cases: (i) strongly convex and Lipschitz-smooth objective function and (ii) convex but…