Related papers: Linear programming problems for l_1- optimal front…
Recent quasi-optimal error estimates for the finite element approximation of total-variation regularized minimization problems require the existence of a Lipschitz continuous dual solution. We discuss the validity of this condition and…
We study optimal procedures for estimating a linear functional based on observational data. In many problems of this kind, a widely used assumption is strict overlap, i.e., uniform boundedness of the importance ratio, which measures how…
The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…
We study integration and $L^2$-approximation in the worst-case setting for deterministic linear algorithms based on function evaluations. The underlying function space is a reproducing kernel Hilbert space with a Gaussian kernel of tensor…
Quantifying extra functions, herein referred to as outcome functions, over optimal solutions of an optimization problem can provide decision makers with additional information on a system. This bears more importance when the optimization…
We introduce LiPopt, a polynomial optimization framework for computing increasingly tighter upper bounds on the Lipschitz constant of neural networks. The underlying optimization problems boil down to either linear (LP) or semidefinite…
We devise and analyze a reliable and efficient a posteriori error estimator for a semilinear control-constrained optimal control problem in two and three dimensional Lipschitz, but not necessarily convex, polytopal domains. We consider a…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we…
This paper studies the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
We derive a linear programming bound on the maximum cardinality of error-correcting codes in the sum-rank metric. Based on computational experiments on relatively small instances, we observe that the obtained bounds outperform all…
This paper develops a frequentist solution to the functional calibration problem, where the value of a calibration parameter in a computer model is allowed to vary with the value of control variables in the physical system. The need of…
We study the optimal approximation of the solution of an operator equation by certain n-term approximations with respect to specific classes of frames. We study worst case errors and the optimal order of convergence and define suitable…
$\renewcommand{\Re}{\mathbb{R}}$ We develop a general randomized technique for solving "implic it" linear programming problems, where the collection of constraints are defined implicitly by an underlying ground set of elements. In many…
Inverse optimization is the problem of determining the values of missing input parameters for an associated forward problem that are closest to given estimates and that will make a given target vector optimal. This study is concerned with…
Identification of model parameters in computer simulations is an important topic in computer experiments. We propose a new method, called the projected kernel calibration method, to estimate these model parameters. The proposed method is…
We present a data-driven method for computing approximate forward reachable sets using separating kernels in a reproducing kernel Hilbert space. We frame the problem as a support estimation problem, and learn a classifier of the support as…
Feature maps associated with positive definite kernels play a central role in kernel methods and learning theory, where regularity properties such as Lipschitz continuity are closely related to robustness and stability guarantees. Despite…
Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…