Efficient faces of a polytope: Interior methods in multiobjective optimization
Abstract
This dissertation addresses the problem of computing the set of efficient faces of a bounded polyhedron in R$\sp{\rm n}$ that is defined by linear inequalities. It describes two algorithms. One algorithm is an interior point method that generalizes and extends the recent path following techniques in Linear Programming to multiple objective optimization. It finds an efficient face in polynomial time. The other algorithm is based on an entirely new approach to multiple objective optimization that employs techniques of algebraic geometry related to the parametrization of algebraic varieties in n-dimensional spaces. It approximates a portion of the set of efficient faces by an algebraic surface. Generalizations for nonlinear multiobjective optimization problems where the feasible region is defined by quadratic constraints are also examined. Parametrization of hyperellipsoids in n space are also studied along with their use in approximating efficient faces (efficient frontier) of polytopes. Relations with multivalued dynamical systems are also discussed.
Degree
Ph.D.
Advisors
Morin, Purdue University.
Subject Area
Industrial engineering
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.