Related papers: Calculus for directional limiting normal cones and…

We identity the optimal non-infinitesimal direction of descent for a convex function. An algorithm is developed that can theoretically minimize a subset of (non-convex) functions.

Motivated by extending the functional stochastic calculus, to important functionals to which it does not apply, a notion of functional derivative along a curve is introduced. This new setting is developed by incorporating path-dependent…

We consider an ordinary nonlinear differential equation with generalized coefficients as an equation in differentials in algebra of new generalized functions. Then the solution of such equation will be a new generalized function. In the…

We propose a novel foundation for calculus that focuses on the notion of approximations while avoiding the use of limits altogether. Continuity is defined as approximation at a point, while differentiability is defined as approximation with…

A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a…

We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods. In particular, we provide necessary…

The question of defining unique, generally applicable constrained second, and higher-order, derivatives is investigated. It is shown that second-order constrained derivatives obtained via two successive constrained differentiations provide…

This paper is devoted to the study of generalized differentiation properties of the infimal convolution. This class of functions covers a large spectrum of nonsmooth functions well known in the literature. The subdifferential formulas…

A non-classical differential calculus on the quantum disc and cones is constructed and the associated integral is calculated.

This paper is devoted to the study of a newly introduced tool, projectional coderivatives and the corresponding calculus rules in finite dimensions. We show that when the restricted set has some nice properties, more specifically, is a…

Differential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for Differential Linear Logic…

In the present paper, classical tools of convex analysis are used to study the solution set to a certain class of set-inclusive generalized equations. A condition for the solution existence and global error bounds is established, in the…

In this paper directional derivative sets and differentials of a given set valued map are studied. Relations between the set valued map and compact subsets of the directional derivative sets of the given map are investigated. Upper and…

A large number matrix optimization problems are described by orthogonally invariant norms. This paper is devoted to the study of variational analysis of the orthogonally invariant norm cone of symmetric matrices. For a general orthogonally…

We extend results of our previous papers, on ordinary multiple points of curves, and on the computation of their conductor, to ordinary multiple subvarieties of codimension one.

In this paper, which is a follow-up of our first paper "Normal forms for ordinary differential operators, I", we extend the theory of normal forms for non-commuting operators, and obtain as an application a commutativity criterion for…

A new directional derivative and a new subdifferential for set-valued convex functions are constructed, and a set-valued version of the so-called 'max-formula' is proven. The new concepts are used to characterize solutions of convex…

In this paper, we study constraint qualifications for the nonconvex inequality defined by a proper lower semicontinuous function. These constraint qualifications involve the generalized construction of normal cones and subdifferentials.…

In this paper, we study the convergence for solutions to a sequence of (possibly degenerate) stochastic differential equations with jumps, when the coefficients converge in some appropriate sense. Our main tools are the superposition…

We consider smooth stochastic convex optimization problems in the context of algorithms which are based on directional derivatives of the objective function. This context can be considered as an intermediate one between derivative-free…