Floyd J. Gould

Stability in Nonlinear Programming

This paper establishes necessary and sufficient conditions for constraint set stability requiring neither convex constraint functions not convex constraint sets. These conditions then lead to a sufficiency result for the continuity of the optimal objective values as the right-hand side varies. Applications to quasiconvex functions are presented.

Exact penalty functions in nonlinear programming

In this paper some new theoretic results on piecewise differentiable exact penalty functions are presented. Sufficient conditions are given for the existence of exact penalty functions for inequality constrained problems more general than concave and several classes of such functions are presented.

Geometry of optimality conditions and constraint qualifications

Certain types of necessary optimality conditions for mathematical programming problems are equivalent to corresponding regularity conditions on the constraint set. For any problem, a certain natural optimality condition, dependent upon the particular constraint set, is always satisfied. This condition can be strengthened in numerous ways by invoking appropriate regularity assumptions on the constraint set. Results are presented for Euclidean spaces and some extensions to Banach spaces are given.

Proximate linear programming: A variable extreme point method

The method of proximate linear programming is relevant for problems in which exact solutions are not required. The method is an edge following algorithm which allows for larger than usual steps by examining basic rather than basic feasible solutions. The algorithm is presented along with computational comparisons with the ordinary simplex method. The relative performance of the new method is most dramatic for problems with dense positive matrices. An extension is proposed for large scale problems with sparse matrices.

Nonlinear Pricing: Applications to Concave Programming

This paper introduces approximation theorems for using nonlinear pricing techniques to solve concave programs, and then proposes an algorithm that is essentially a sequential unconstrained procedure with exponential prices. Then it derives upper bounding estimates and solves several specific problems.

On using equality-constraint algorithms for inequality constrained problems

Abstract : The paper discusses several theoretic aspects of replacing inequality constrained problems with an appropriate equality constrained problem. It is shown that such a replacement may be neither valid nor advantageous. (Author)

Technical Note-A Note on Extended GLM

This note presents a modification of some earlier work of Gould on nonlinear multiplier functions in generalized Lagrangian penalty formulations. The purpose of the modification is to present a generalized Lagrangian that is invariant under right-hand-side translations and that yields the usual economic interpretation for unused resource quantities at optimality.