Mathematical Programming: Series A and B

Second-order necessary conditions in nonlinear programming are derived by a new method that does not require the usual sort of constraint qualification. In terms of the multiplier vectors appearing in such second-order conditions, an estimate, is ...

A Halin graphH=TźC is obtained by embedding a treeT having no nodes of degree 2 in the plane, and then adding a cycleC to join the leaves ofT in such a way that the resulting graph is planar. These graphs are edge minimal 3-connected, hamiltonian, and ...

This paper is concerned with iterative methods for the linear complementarity problem (LCP) of findingx and y in Rn such thatc+Dx+yź0, b-xź0, andxT(c+Dx+y)=yT(b-x)=0 whenb>0. This is the LCP (M, q) withM=(l 0D t), which is in turn equivalent to a linear ...

We show that Van der Heyden's variable dimension algorithm and Dantzig and Cottle's principal pivoting method require 2n---1 pivot steps to solve a class of linear complementarity problems of ordern. Murty and Fathi have previously shown that the ...

The procedure samples the efficient set by computing the nondominated criterion vector that is closest to an ideal criterion vector according to a randomly weighted Tchebycheff metric. Using `filtering' techniques, maximally dispersed representatives of ...

The fractional program P is defined by maxf(x)/g(x) subject toxźX. A class of methods for solving P is based on the auxiliary problem Q(ź) with a parameter ź: maxf(x)źźg(x) subject toxźX. Starting with two classical methods in this class, the Newton ...