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Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been…
Existing results on decomposition methods and algorithms for nonconvex problems are minimal. Parallel decomposition algorithms do not exist for nonconvex problems with coupling nonlinear equality constraints. Besides, decomposition…
Border complexity captures functions that can be approximated by low-complexity ones. Debordering is the task of proving an upper bound on some non-border complexity measure in terms of a border complexity measure, thus getting rid of…
This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…
Predefined-time stability enables convergence within a user-specified time independent of initial conditions. Existing results are predominantly based on autonomous Lyapunov inequalities, where the predefined-time is realized through…
Consistency training regularizes a model by enforcing predictions of original and perturbed inputs to be similar. Previous studies have proposed various augmentation methods for the perturbation but are limited in that they are agnostic to…
By employing non-equispaced grid points near boundaries, boundary-optimized upwind finite-difference operators of orders up to nine are developed. The boundary closures are constructed within a diagonal-norm summation-by-parts (SBP)…
It is proved in Chon{\'e} and Le Meur (2001) that the problem of minimizing a Dirichlet-like functional of the function $u\_h$ discretized with $P\_1$ Finite Elements, under the constraint that $u\_h$ be convex, cannot converge. Here, we…
The constraint-preserving approach, which aim is to provide consistent boundary conditions for Numerical Relativity simulations, is discussed in parallel with other recent developments. The case of the Z4 system is considered, and…
We present a novel direct transcription method to solve optimization problems subject to nonlinear differential and inequality constraints. We prove convergence of our numerical method under reasonably mild assumptions: boundedness and…
This paper is concerned with the study of constrained statistical learning problems, the unconstrained version of which are at the core of virtually all of modern information processing. Accounting for constraints, however, is paramount to…
We have previously reported a Bayesian algorithm for determining the coordinates of points in three-dimensional space from uncertain constraints. This method is useful in the determination of biological molecular structure. It is limited,…
For linear recurrence systems, the problem of finding rational solutions is reduced to the problem of computing polynomial solutions by computing a content bound or a denominator bound. There are several bounds in the literature. The…
Dynamic nonlinear systems exhibit distortions arising from coupled static and dynamic effects. Their intertwined nature poses major challenges for data-driven modeling. This paper presents a theoretical framework grounded in structured…
We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
The focus of this paper is on causal consistency in a {\em partially replicated} distributed shared memory (DSM) system that provides the abstraction of shared read/write registers. Maintaining causal consistency in distributed shared…