Showing papers on "Concave function published in 1986"

Methods for global concave minimization: A bibliographic survey

Abstract: The global concave minimization problem is to find the constrained global minimum of a concave function. Since such a function may have many local minima, finding the global minimum is a computationally difficult problem. In this bibliographic survey, which includes most of the recent papers on constrained global concave minimization, we have attempted to briefly summarize the main ideas in each paper. These recent papers include those concerned with large scale global concave minimization and bilinear programming.

Concavity of the quarkonium potential.

Abstract: The heavy-quark--antiquark potential is shown to be a monotone nondecreasing and concave function of the separation. This property holds independent of the gauge group and the details of the matter sector.

Mathematical Programming: An Introduction to Optimization

Abstract: 1. An Introduction to Mathematical Programming 2. Subspaces, Matrices, Affine Sets, Cones, Convex Sets, and the Linear Programming Problem 3. The Primal Simplex Procedure 4. Duality and the Linear Complementarity Problem 5. Other Simplex Procedures 6. Network Programming 7. Convex and Concave Functions 8. Optimality Conditions 9. Search Techniques for Unconstrained Optimization Problems 10. Penalty Function Methods

Concave Minimization Via Collapsing Polytopes

Abstract: We present a procedure for globally minimizing a concave function over a bounded polytope by successively minimizing the function over polytopes containing the feasible region, and collapsing to the feasible region. The initial containing polytope is a simplex, and, at the kth iteration, the procedure chooses the most promising vertex of the current containing polytope to refine the approximation. The method generates a tree whose ultimate terminal nodes coincide with the vertices of the feasible region, and accounts for the vertices of the containing polytopes.

On minimizing the sum of a convex function and a concave function

Abstract: We consider here the problem of minimizing a particular subclass of quasidifferentiable functions: those which may be represented as the sum of a convex function and a concave function. It is shown that in an n-dimensional space this problem is equivalent to the problem of minimizing a concave function on a convex set. A successive approximations method is suggested; this makes use of some of the principles of ∈-steepest-descent-type approaches.

A method for minimizing the sum of a convex function and a continuously differentiable function

Abstract: This paper presents a method for minimizing the sum of a possibly nonsmooth convex function and a continuously differentiable function. As in the convex case developed by the author, the algorithm is a descent method which generates successive search directions by solving quadratic programming subproblems. An inexact line search ensures global convergence of the method to stationary points.

Midpoint convex functions majorized by midpoint concave functions

Abstract: Theoreme de representation pour les fonctions convexes medianes et les fonctions concaves medianes satisfaisant a une inegalite

A Robust Approach to Equilibrium Yield Curves

Abstract: The surplus yield models of fisheries management usually assume that a concave function of equilibrium yield versus fishing effort exists. However, this function is notoriously difficult to fit to real data for a number of reasons, including the fact that few fisheries are in equilibrium. A procedure for obtaining rough estimates of these equilibrium curves is introduced. Management strategies based on these estimates and the annual yield curves are also presented. The procedures are then applied to several fish stocks.