Related papers: Monotone smoothing splines with bounds
Here a mixed problem for a nonlinear hyperbolic equation with Neumann boundary value condition is investigated, and a priori estimations for the possible solutions of the considered problem are obtained. These results demonstrate that any…
We detail a simple procedure (easily convertible to an algorithm) for constructing from quasi-uniform samples of $f$ a sequence of linear spline functions converging to the monotone rearrangement of $f$, in the case where $f$ is an almost…
Variational inequalities are a universal optimization paradigm that is interesting in itself, but also incorporates classical minimization and saddle point problems. Modern realities encourage to consider stochastic formulations of…
We consider a method of pairwise variations for smooth optimization problems, which involve polyhedral constraints. It consists in making steps with respect to the difference of two selected extreme points of the feasible set together with…
Robust optimization is one of the fundamental approaches to deal with uncertainty in combinatorial optimization. This paper considers the robust spanning tree problem with interval data, which arises in a variety of telecommunication…
In many classification problems it is desirable to output well-calibrated probabilities on the different classes. We propose a robust, non-parametric method of calibrating probabilities called SplineCalib that utilizes smoothing splines to…
Spectral clustering is a broad class of clustering procedures in which an intractable combinatorial optimization formulation of clustering is "relaxed" into a tractable eigenvector problem, and in which the relaxed solution is subsequently…
Unconstrained optimization problems become more common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical methods for solving them more quickly and efficiently have been…
In this paper, we propose a scaled gradient modified non-monotone line search method for solving constrained minimization problems, and explore several specific properties of this method, namely, its convergence analysis. We discuss the…
The first order condition of the constrained minimization problem leads to a saddle point problem. A multigrid method using a multiplicative Schwarz smoother for saddle point problems can thus be interpreted as a successive subspace…
Let (M,g) be a smooth compact, n dimensional Riemannian manifold,with smooth n-1 dimensional boundary. We prove that the stable critical points of the mean curvature of the boundary generates solutions for a singularly perturbed elliptic…
We discuss a number of estimates of the hazard under the assumption that the hazard is monotone on an interval [0,a]. The usual isotonic least squares estimators of the hazard are inconsistent at the boundary points 0 and a. We use…
A method of optimal control computation is proposed for problems with control and state constraints. It uses a sequence of control structure adjustments in the form of generations and reductions of nodes and arcs, which do not change the…
Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…
We study a free boundary problem on the lattice whose scaling limit is a harmonic free boundary problem with a discontinuous Hamiltonian. We find an explicit formula for the Hamiltonian, prove the solutions are unique, and prove that the…
In areas such as kernel smoothing and non-parametric regression there is emphasis on smooth interpolation and smooth statistical models. Splines are known to have optimal smoothness properties in one and higher dimensions. It is shown, with…
Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
We consider the problem of minimizing a sum of non-convex functions over a compact domain, subject to linear inequality and equality constraints. Approximate solutions can be found by solving a convexified version of the problem, in which…
We extend the adaptive regression spline model by incorporating saturation, the natural requirement that a function extend as a constant outside a certain range. We fit saturating splines to data using a convex optimization problem over a…