Interior-point methods in augmented form for linear and convex quadratic programming require the solution of a sequence of symmetric indefinite linear systems which are used to derive search directions. Safeguards are typically required in order to handle free variables or rank-deficient Jacobians. We propose a consistent framework and accompanying theoretical justification for regularizing the...

A typical iteration starts at the current point x where nz (say) variables are free from both their bounds. The projected gradient vector gz, whose elements are the derivatives of F ðxÞ with respect to the free variables, is known. A unit lower triangular matrix L and a diagonal matrix D (both of dimension nz), such that LDL is a positive-definite approximation of the matrix of second derivativ...

In this paper, bi-matrix games are investigated based on L-R fuzzy variables. Also, based on the fuzzy max order several models in non-symmetrical L-R fuzzy environment is constructed and the existence condition of Nash equilibrium strategies of the fuzzy bi-matrix games is proposed. At last, based on the Nash equilibrium of crisp parametric bi-matrix games, we obtain the Pareto and weak Pareto...

ions which did not contain assignments to their formalparameters, but the necessary changes to the predicates are ex­tensive and do not yield a wider class of computations: if I isnot covertly assigned to in L 2.5.3 establishes that E is equivalentto e[E](i\I'.I'=I~false,tpue), and thus a version of 2.5.4 confirms that fnI.E can be replaced by fnI .• E, which we allow in any cas...