J. G. Ecker

Generating all maximal efficient faces for multiple objective linear programs

A method for generating the entire efficient set for a multiple objective linear program is developed. The method is based on two characterizations of maximal efficient faces. The first characterization is used to determine the set of maximal efficient faces incident to a given efficient vertex, and the second characterization ensures that previously generated maximal efficient faces are easily recognized (and not regenerated). The efficient set is described as the union of maximal efficient faces. An alternate implicit description of the efficient set as the set of all optimal vectors for a finite set of linear programs is also provided.

Optimizing a linear function over an efficient set

AbstractThe problem (P) of optimizing a linear functiondTx over the efficient set for a multiple-objective linear program (M) is difficult because the efficient set is typically nonconvex. Given the objective function directiond and the set of domination directionsD, ifdTπ≧0 for all nonzero π∈D, then a technique for finding an optimal solution of (P) is presented in Section 2. Otherwise, given a current efficient point

Optimal Design of a Dry-Type Natural-Draft Cooling Tower by Geometric Programming

\hat x

A Reduced Gradient-method for Quadratic Programs With Quadratic Constraints and Lp-constrained Lp-approximation Problems

, if there is no adjacent efficient edge yielding an increase indTx, then a cutting plane

A modified reduced gradient method for dual posynomial programming

d^T x = d^T \hat x

Solving Bilevel Linear Programs Using Multiple Objective Linear Programming

is used to obtain a multiple-objective linear program (