Joseph G. Ecker

Finding all efficient extreme points for multiple objective linear programs

In this paper we develop a method for finding all efficient extreme points for multiple objective linear programs. Simple characterizations of the efficiency of an edge incident to a nondegenerate or a degenerate efficient vertex are given. These characterizations form the basis of an algorithm for enumerating all efficient vertices. The algorithm appears to have definite computational advantages over other methods. Some illustrative examples are included.

An ellipsoid algorithm for nonlinear programming

We investigate an ellipsoid algorithm for nonlinear programming. After describing the basic steps of the algorithm, we discuss its computer implementation and present a method for measuring computational efficiency. The computational results obtained from experimenting with the algorithm are discussed and the algorithms performance is compared with that of a widely used commercial code.

Geometric Programming: Duality in Quadratic Programming and

The duality theory of geometric programming as developed by Duflin, Peterson and Zener [7] is based on abstract properties shared by certain classical inequalities, such as Cauchy’s arithmetic-geometric mean inequality and Holder’s inequality. Inequalities with these abstract properties have been termed “geometric inequalities” [7, p. 195]. In this sequence of papers [15], [16], [17] a new geometric inequality is established and used to extend the “refined duality theory” for “posynomial” geometric programs [6] and [7, Chap. VI]. This extended duality theory treats both “quadratically-constrained quadratic programs” and “

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-Approximation II (Canonical Programs)

-constrained

Reversed geometric programming: A branch-and-bound method involving linear subproblems

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Solving nonlinear principal-agent problems using bilevel programming

-approximation (regression) problems” through a rather novel and unified formulation of these two classes of programs. This work generalizes some of the work of others on (linearly-constrained) quadratic programs and provides a new explicit formulation of duality for constrained approximation problems. Duality theories have been developed for a large class of prog...

An application of nonlinear optimization in molecular biology

Abstract The paper proposes a branch-and-bound method to find the global solution of general polynomial programs. The problem is first transformed into a reversed posynomial program. The procedure, which is a combination of a previously developed branch-and-bound method and of a well-known cutting plane algorithm, only requires the solution of linear subproblems.

A class of rank-two ellipsoid algorithms for convex programming

While significant progress has been made, analytic research on principal-agent problems that seek closed-form solutions faces limitations due to tractability issues that arise because of the mathematical complexity of the problem. The principal must maximize expected utility subject to the agent’s participation and incentive compatibility constraints. Linearity of performance measures is often assumed and the Linear, Exponential, Normal (LEN) model is often used to deal with this complexity. These assumptions may be too restrictive for researchers to explore the variety of relationships between compensation contracts offered by the principal and the effort of the agent. In this paper we show how to numerically solve principal-agent problems with nonlinear contracts. In our procedure, we deal directly with the agent’s incentive compatibility constraint. We illustrate our solution procedure with numerical examples and use optimization methods to make the problem tractable without using the simplifying assumptions of a LEN model. We also show that using linear contracts to approximate nonlinear contracts leads to solutions that are far from the optimal solutions obtained using nonlinear contracts. A principal-agent problem is a special instance of a bilevel nonlinear programming problem. We show how to solve principal-agent problems by solving bilevel programming problems using the ellipsoid algorithm. The approach we present can give researchers new insights into the relationships between nonlinear compensation schemes and employee effort.

Performance of several optimization methods on robot trajectory planning problems

Abstract A maximum likelihood approach has been proposed for finding protein binding sites on strands of DNA [G.D. Stormo, G.W. Hartzell, Proceedings of the National Academy of Sciences of the USA 86 (1989) 1183]. We formulate an optimization model for the problem and present calculations with experimental sequence data to study the behavior of this site identification method.