SADDLE POINT CRITERIA AND THE EXACT MINIMAX PENALTY FUNCTION METHOD IN NONCONVEX PROGRAMMING

Path following in the exact penalty method of convex programming

Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, ...

Saddle Point Criteria and Duality in Multiobjective Programming via an Η-approximation Method

In this paper, Antczak’s -approximation approach is used to prove the equivalence between optima of multiobjective programming problems and the -saddle points of the associated -approximated vector optimisation problems. We introduce an -Lagrange function for a constructed -approximated vector optimisation problem and present some modified -saddle point results. Furthermore, we construct an -ap...

The l1 exact G-penalty function method and G-invex mathematical programming problems

An exact primal-dual penalty method approach to warmstarting interior-point methods for linear programming

One perceived deficiency of interior-point methods in comparison to active set methods is their inability to efficiently re-optimize by solving closely related problems after a warmstart. In this paper, we investigate the use of a primal-dual penalty approach to overcome this problem. We prove exactness and convergence and show encouraging numerical results on a set of linear and mixed integer ...

SADDLE POINT VARIATIONAL METHOD FOR DIRAC CONFINEMENT

A saddle point variational (SPV ) method was applied to the Dirac equation as an example of a fully relativistic equation with both negative and positive energy solutions. The effect of the negative energy states was mitigated by maximizing the energy with respect to a relevant parameter while at the same time minimizing it with respect to another parameter in the wave function. The Cornell pot...