This paper describes formulation and management of constraints, and a nonlinear optimization algorithm that together enable interactive geometrically aware manipulation of articulated objects. Going beyond purely kinematic or dynamic approaches, our solution method directly employs geometric constraints to ensure noninterpenetration during object manipulation. We present the formulation of the ...

We examine a multidimensional optimisation problem in the tropical mathematics setting. The problem involves the minimisation of a nonlinear function defined on a finite-dimensional semimodule over an idempotent semifield subject to linear inequality constraints. We start with an overview of known tropical optimisation problems with linear and nonlinear objective functions. A short introduction...

In this paper, we present a power penalty function approach to the linear complementarity problem arising from pricing American options. The problem is first reformulated as a variational inequality problem; the resulting variational inequality problem is then transformed into a nonlinear parabolic partial differential equation (PDE) by adding a power penalty term. It is shown that the solution...

We consider a family of Gagliardo-Nirenberg-Sobolev interpolation inequalities which interpolate between Sobolev’s inequality and the logarithmic Sobolev inequality, with optimal constants. The difference of the two terms in the interpolation inequalities (written with optimal constant) measures a distance to the manifold of the optimal functions. We give an explicit estimate of the remainder t...

The attracting set of dynamical systems have been extensively studied over the past few decades and various results are reported. It is well known that one of the most researching tools is inequality technique. With the establishment of various differential and integral inequalities 1–12 , the sufficient conditions on the attracting sets for different differential systems are obtained 12–16 . H...

We consider a multidimensional extremal problem formulated in terms of tropical mathematics. The problem is to minimize a nonlinear objective function, which is defined on a finite-dimensional semimodule over an idempotent semifield, subject to linear inequality constraints. An efficient solution approach is developed which reduces the problem to that of solving a linear inequality with an exte...

Abstract: Recently, nonlinear H∞ control theory has been paid attention for the powerful design method for a robust stabilization. The solvable condition of nonlinear H∞ control problem is given by the Hamilton Jacobi Inequality (HJI). The HJI is the partial differential inequality which is quite difficult to solve, so some numerical approaches have been researched. The approach to solve the HJ...

In this paper, we consider a class of discrete time optimal control problems with time delay and subject to nonlinear all-time-step inequality constraints on both the state and control. By using a constraint transcription technique in conjunction with a local smoothing method, the problem is approximated by a sequence of discrete time optimal control problems with time delay and subject to nonl...