Nonsmoothness in dynamic process models can hinder conventional methods for simulation, sensitivity analysis, and optimization, and can be introduced, for example, by transitions in flow regime or thermodynamic phase, or through discrete changes in the operating mode of a process. While dedicated numerical methods exist for nonsmooth problems, these methods require generalized derivative inform...

Generalized second–order directional derivatives for nonsmooth real–valued functions are studied and their connections with second–order variational sets are investigated. A necessary second–order optimality condition for problems with inequality constraints is obtained.

We present some error bound results of generalized D-gap functions for nonsmooth and nonmonotone variational inequality (VI) problems. Application is given in providing a derivative-free descent method.

We consider a proximal algorithm with quasi distance applied to nonconvex and nonsmooth functions involving analytic properties for an unconstrained minimization problem. We show the behavioral importance of this proximal point model for habit’s formation in Decision and Making Sciences.

1. Abstract Practical optimization problems often involve nonsmooth functions of hundreds or thousands of variables. As a rule, the variables in such large problems are restricted to certain meaningful intervals. In the report [Haarala, Mäkelä, 2006] we have described an efficient adaptive limited memory bundle method for large-scale nonsmooth, possibly nonconvex, bound constrained optimization...

This paper discusses dynamical systems for disk-covering and sphere-packing problems. We present facility location functions from geometric optimization and characterize their differentiable properties. We design and analyze a collection of distributed control laws that are related to nonsmooth gradient systems. The resulting dynamical systems promise to be of use in coordination problems for n...

We present a new proximity control bundle algorithm to minimize nonsmooth and nonconvex locally Lipschitz functions. In contrast with the traditional oracle-based methods in nonsmooth programming, our method is model-based and can accommodate cases where several Clarke subgradients can be computed at reasonable cost. We propose a new way to manage the proximity control parameter, which allows u...

This paper is concerned with the spline interpolation of functions with a boundary layer component. It is shown that polynomial formulas of spline interpolation for such functions lead to significant errors. We proposed nonpolynomial spline interpolation formulas, fitted to a boundary layer component. Nonsmooth and smooth on whole interval interpolants are constructed. The accuracy of construct...

An algorithm is developped for minimizing nonsmooth convex functions. This algortithm extends Elzinga-Moore cutting plane algorithm by enforcing the search of the next test point not too far from the previous ones, thus removing compactness assumption. Our method is to Elzinga-Moore’s algorithm what a proximal bundle method is to Kelley’s algorithm. As in proximal bundle methods, a quadratic pr...