Related papers: Second-order analysis of piecewise linear function…
Wilson lines, being comparators that render non-local operator products gauge invariant, are extensively used in QCD calculations, especially in small-$x$ calculations, calculations concerning validation of factorisation schemes and in…
This work provides a systematic study of the variational properties of decomposable functions which are compositions of an outer support function and an inner smooth mapping under certain constraint qualifications. A particular focus is put…
Fractional difference equations provide a flexible mathematical framework for modeling complex systems with memory, hereditary, and non-local effects. In this work, we study the stability of higher-order two-term fractional linear…
We study a class of nonlinear eigenvalue problems which involves a convolution operator as well as a superlinear nonlinearity. Our variational existence proof is based on constrained optimization and provides a one-parameter family of…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
The main result of the paper is on the continuity of weak solutions of infinitely degenerate quasilinear second order equations. Namely, we show that every weak solution to a certain class of degenerate quasilinear equations is continuous.…
This paper is concerned with incremental stability properties of nonlinear systems. We propose conditions to compute an upper bound on the incremental L2-gain and to assess incremental asymptotic stability of piecewise-affine (PWA) systems.…
In this paper we study local Hamiltonian operators for multi-component evolutionary differential-difference equations. We address two main problems: the first one is the classification of low order operators for the two-component case. On…
We discuss the (first- and second-order) optimality conditions for nonlinear programming under the relaxed constant rank constraint qualification. This condition generalizes the so-called linear independence constraint qualification.…
We prove the existence of minimizers for functionals defined over the class of convex domains contained inside a bounded set D of R^N and with prescribed volume. Some applications are given, in particular we prove that the eigenvalues of…
We distinguish two kinds of piecewise linear functions and provide an interesting representation for a piecewise linear function between two normed spaces. Based on such a representation, we study a fully piecewise linear vector…
We consider the problem of designing piecewise affine policies for two-stage adjustable robust linear optimization problems under right-hand side uncertainty. It is well known that a piecewise affine policy is optimal although the number of…
In this paper, we have considered second order non-homogeneous linear differential equations having entire coefficients. We have established conditions ensuring non-existence of finite order solution of such type of differential equations.
Fitting a matrix of a given rank to data in a least squares sense can be done very effectively using 2nd order methods such as Levenberg-Marquardt by explicitly optimizing over a bilinear parameterization of the matrix. In contrast, when…
This paper continues earlier work and is concerned with the inverse problem of parameter identification in variational inequalities of the second kind that does not only treat the parameter linked to a bilinear form, but importantly also…
This paper is devoted to developing and applications of a generalized differential theory of variational analysis that allows us to work in incomplete normed spaces, without employing conventional variational techniques based on…
Second order approximate ancillaries have evolved as the primary ingredient for recent likelihood development in statistical inference. This uses quantile functions rather than the equivalent distribution functions, and the intrinsic…
We propose adaptive, line search-free second-order methods with optimal rate of convergence for solving convex-concave min-max problems. By means of an adaptive step size, our algorithms feature a simple update rule that requires solving…
In this paper we give refinements of some convex and log-convex moment inequalities of the first and second order using a special kind of positive semi-definite form. An open problem concerning eight parameter refinement of second order is…
In this note, we focus on smooth nonconvex optimization problems that obey: (1) all local minimizers are also global; and (2) around any saddle point or local maximizer, the objective has a negative directional curvature. Concrete…