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Over the last decade, approximating functions in infinite dimensions from samples has gained increasing attention in computational science and engineering, especially in computational uncertainty quantification. This is primarily due to the…
We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of…
Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind…
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…
Submodular functions are a fundamental object of study in combinatorial optimization, economics, machine learning, etc. and exhibit a rich combinatorial structure. Many subclasses of submodular functions have also been well studied and…
Submodular functions and their optimization have found applications in diverse settings ranging from machine learning and data mining to game theory and economics. In this work, we consider the constrained maximization of a submodular…
This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate. The approach extends max-affine methods from convex shape-restricted…
The Sinc approximation is a function approximation formula that attains exponential convergence for rapidly decaying functions defined on the whole real axis. Even for other functions, the Sinc approximation works accurately when combined…
The self-consistent expansion (SCE) is a powerful technique for obtaining perturbative solutions to problems in statistical physics but it suffers from a subtle problem - too much freedom! The SCE can be used to generate an enormous number…
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…
We study the problem of approximating and learning coverage functions. A function $c: 2^{[n]} \rightarrow \mathbf{R}^{+}$ is a coverage function, if there exists a universe $U$ with non-negative weights $w(u)$ for each $u \in U$ and subsets…
Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
A simple and very accurate method to approximate a function with a finite number of discontinuities is presented. This method relies on hyperbolic tangent functions of rational arguments as connecting functions at the discontinuities, each…
This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions…
We consider finite horizon reach-avoid problems for discrete time stochastic systems. Our goal is to construct upper bound functions for the reach-avoid probability by means of tractable convex optimization problems. We achieve this by…
Solutions to network optimization problems have greatly benefited from developments in nonlinear analysis, and, in particular, from developments in convex optimization. A key concept that has made convex and nonconvex analysis an important…
Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…
We consider the \mnk{classical} problem of a controller activating (or sampling) sequentially from a finite number of $N \geq 2$ populations, specified by unknown distributions. Over some time horizon, at each time $n = 1, 2, \ldots$, the…
Let $G$ be a nonempty bounded domain in a finite-dimensional Euclidean space. The main results are general estimates from below at points from $G$ for an arbitrary subharmonic function $u\not\equiv -\infty$ on the closure of the domain $G$…