Using the “basic monotonicity property” along locally admissible trajectories, we extend to very general problems certain existing results concerning the differential inequalities verified by the value function of an optimal control problem; these differential inequalities are expressed in terms of its contingent, quasitangent, and peritangent (Clarke’s) directional derivatives and in terms of ...

Classical gradient systems have a linear relation between rates and driving forces. In generalized gradient systems we allow for arbitrary relations derived from general non-quadratic dissipation potentials. This paper describes two natural origins for these structures. A first microscopic origin of generalized gradient structures is given by the theory of large-deviation principles. While Mark...

its neighbours, above and below. A good rule is that the space between any two pavilions should be about equal to 1^ times the height of such pavilions?thus if a pavilion be 75 feet high, the distance between it and its neighbour should be not less than 90 to 100 feet. The pavilions may be built radiating like the spokes of a wheel (like several of the Central Jails in India) or in form of a ho...

In this paper, a size-dependent first-order shear deformation plate model is formulated in the framework of the higher-order generalized nonlocal strain-gradient (GNSG) theory. This modelemploys ...

We analyze the optimal value function v associated with a general parametric optimization problem via theory of viscosity solutions. The novelty is that we obtain regularity properties by showing it solution to set first-order equations. As consequence, in Banach spaces, provide sufficient conditions for local and global Lipschitz v. also derive, finite dimensions, optimality through comparison...

Combining the techniques of the working set identification and generalized gradient projection, we present a new generalized gradient projection algorithm for minimax optimization problems with inequality constraints. In this paper, we propose a new optimal identification function, from which we provide a new working set. At each iteration, the improved search direction is generated by only one...

The smoothing procedure has been introduced by Schh onauer as an acceleration algorithm for the Generalized Conjugate Gradient methods. In this paper, after giving our deenition of Conjugate Gradient type methods, and using a Generalized Hessenberg process, we introduce a Hybrid generalized Conjugate Gradient type method. We show that this Hybrid procedure is a variable smoothing procedure. And...

Subgradient and Newton algorithms for nonsmooth optimization require generalized derivatives to satisfy subtle approximation properties: conservativity the former semismoothness latter. Though these two properties originate in entirely different contexts, we show that semi-algebraic setting they are equivalent. Both a derivative simply it coincide with standard directional on tangent spaces of ...