A direct method for the computation of polynomial conservation laws of polynomial systems of nonlinear partial differential equations (PDEs) in multi-dimensions is presented. The method avoids advanced differential-geometric tools. Instead, it is solely based on calculus, variational calculus, and linear algebra. Densities are constructed as linear combinations of scaling homogeneous terms with...

Milo s Zefran1 and Vijay Kumar2 1California Institute of Technology, Email: [email protected] 2GRASP Laboratory, University of Pennsylvania, Email: [email protected] Abstract In this paper, we argue that it is advantageous to formulate motion planning as a variational problem. In this way, a uni ed framework for addressing redundancy, constraints, and optimality is obtained. An ...

Tutorial topics • A bit of history • Examples of variational methods • A brief intro to graphical models • Variational mean field theory – Accuracy of variational mean field – Structured mean field theory • Variational methods in Bayesian estimation • Convex duality and variational factorization methods – Example: variational inference and the QMR-DT Variational methods • Classical setting: " f...

Various coercivity conditions appear in the literature in order to guarantee solutions for the Variational Inequality Problem. We show that these conditions are equivalent to each other and that they are not only sufficient, but also necessary for the set of solutions to be non-empty and bounded.

In this paper the regularity of one-parametric optimization problems in the sense of Jongen, Jonker and Twilt is extended to one-parametric variational inequalities. The ve singularities are deened in this context and suitable indices are described around them. Many of the local properties of the singularities are also proved for this case. The generic property of the deened class of regular on...

We discuss a smooth variational principle for partially smooth viscosity subdiierentials and explore its applications in nonsmooth analysis. Short Title: Partially smooth variational principles.

Using variational analysis techniques, we study subsmooth multifunctions in Banach spaces. In terms of the normal cones and coderivatives, we provide some characterizations for such multifunctions to be calm. Sharper results are obtained for Asplund spaces. We also present some exact formulas of the modulus of the calmness. As applications, we provide some error bound results on nonconvex inequ...