Search Results

A class of parametric optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints is investigated. The perturbations appear in the objective functional, the state equation and in mixed pointwise ...

This paper is concerned with the stability of minimizers to a parametric optimal control problem governed by semilinear elliptic equations with mixed pointwise control-state constraints. Under the strictly nonnegative second-order optimality ...${}^{\mathrm{}}$${}^{}$

The theoretical and empirical performance of Empirical Risk Minimization (ERM) often suffers when loss functions are poorly behaved with large Lipschitz moduli and spurious sharp minimizers. We propose and analyze a counterpart to ERM called ...

This paper studies local stability of a parametric optimal control problem governed by semilinear elliptic equations with mixed pointwise constraints. We show that if the unperturbed problem satisfies the strictly nonnegative second-order ...${}^{}$

Upper semicontinuous (usc) functions arise in the analysis of maximization problems, distributionally robust optimization, and function identification, which includes many problems of nonparametric statistics. We establish that every usc function ...

Approximation is central to many optimization problems and the supporting theory provides insight as well as foundation for algorithms. In this paper, we lay out a broad framework for quantifying approximations by viewing finite- and infinite-...

This paper delivers a study on the change of rank of input matrix in Extreme Learning Machine (ELM) and the relationship between the rank of input matrix and the residence error of training an ELM. From the viewpoint of data analysis, the study reveals ...

In this paper, a new method for solving the perspective-n-point (PnP) problem is developed. With an auxiliary point, the linear method for the special case of four coplanar points is extended to find the coarse solutions for the general P3P problem. A ...

In the present paper, we will study the solution stability of parametric variational conditions $${{0 \in f(\mu, x)+ N_{K(\lambda)}(x)},}$$ where M and are topological spaces, $${f : M \times R^n \to R^n}$$ is a function, $${K : \Lambda\to 2^{R^n}}$$ is ...