In this paper we present error estimates for kernel interpolation at scattered sites on manifolds. The kernels we consider will be obtained by the restriction of positive definite kernels on Rd, such as radial basis functions, to a smooth, compact embedded submanifold M ⊂ Rd with no boundary. For restricted kernels having finite smoothness, we provide a complete characterization of the native s...

This paper presents a new approach to economic dispatch (ED) problems with nonsmooth cost functions using a particle swarm optimization (PSO) technique. The practical ED problems have nonsmooth cost functions with equality and inequality constraints, which makes the problem of finding the global optimum difficult when using any mathematical approaches. In this paper, a modified PSO (MPSO) mecha...

We propose a unifying framework that combines smoothing approximation with fast first order algorithms for solving nonsmooth convex minimization problems. We prove that independently of the structure of the convex nonsmooth function involved, and of the given fast first order iterative scheme, it is always possible to improve the complexity rate and reach an O(ε−1) efficiency estimate by solvin...

We review the concept of VU-decomposition of nonsmooth convex functions, which is closely related to the notion of partly smooth functions. As VU-decomposition depends on the subdifferential at the given point, the associated objects lack suitable continuity properties (because the subdifferential lacks them), which poses an additional challenge to the already difficult task of constructing sup...

Abstract In this paper, mixed-integer nonsmooth constrained optimization problems are considered, where objective/constraint functions available only as the output of a black-box zeroth-order oracle that does not provide derivative information. A new derivative-free linesearch-based algorithmic framework is proposed to suitably handle those problems. First, scheme for bound combines dense seque...

This paper deals with nonsmooth nonlinear complementarity problem, where the underlying functions are nonsmooth which admit the H-differentiability but not necessarily locally Lipschitzian or directionally differentiable. We consider a reformulation of the nonlinear complementarity problem as an unconstrained minimization problem. We describe Hdifferentials of the associated penalized Fischer-B...

This study addresses some algorithms for solving structured unconstrained convex optimization problems using first-order information where the underlying function includes high-dimensional data. The primary aim is to develop an implementable algorithmic framework for solving problems with multiterm composite objective functions involving linear mappings using the optimal subgradient algorithm, ...