The generalized bilevel programming problem (GBLP) is a bilevel mathematical program
where the lower level is a variational inequality. In this paper we prove that if the objective …

… Qiji Jim Zhu is Professor of Mathematics at Western Michigan University. His email
address is zhu@wmich.edu. … Harvey, Liu, and Zhu [10] argue that there are hundreds of …

We study infinitesimal properties of nonsmooth (nondifferentiable) functions on smooth
manifolds. The eigenvalue function of a matrix on the manifold of symmetric matrices gives a …

Most firms and portfolio managers rely on backtests (or historical simulations of performance)
to select investment strategies and allocate them capital. Standard statistical techniques …

This paper is concerned with the optimality of a trend following trading rule. The idea is to
catch a bull market at its early stage, ride the trend, and liquidate the position at the first …

Nonsmooth analysis had its origins in the early 1970s when control theorists and nonlinear
programmers attempted to deal with necessary optimality conditions for problems with …

Many problems in applied mathematics, such as those in control theory, mathematical
economics, and mechanics. lead to the study of differential inclusions. In a differential inclusion …

This paper discusses Hamiltonian necessary conditions for a nonsmooth multiobjective
optimal control problem with endpoint constraints involving a general preference. The …

We prove a general implicit function theorem for multifunctions with a metric estimate on the
implicit multifunction and a characterization of its coderivative. Traditional open covering …

We develop an extended version of the extremal principle in variational analysis that can be
treated as a variational counterpart to the classical separation results in the case of …