A new method for multi-objective optimization of linear and mixed programs based on Lagrange multiplier methods is developed. The method resembles, but is distinct from, objective function weighting and goal programming methods. A subgradient optimization algorithm for selecting the multipliers is presented and analyzed. The method is illustrated by its application to a model for determining the weekly re-distribution of railroad cars from excess supply areas to excess demand areas, and to a model for balancing cost minimization against order completion requirements for a dynamic lot size model.

Thesis (M.S.)--Kutztown University of Pennsylvania, 2001. / Source: Masters Abstracts International, Volume: 45-06, page: 3171. Typescript. Abstract precedes thesis as preliminary leaves[1-3]. Includes bibliographical references (leaves 91-92).

Thesis (Ph. D.)--Virginia Polytechnic Institute, 1975. / Also available via the Internet.

Thesis (M.App.Sc.) - Carleton University, 2002. / Includes bibliographical references (p. 116-119). Also available in electronic format on the Internet.

Thesis (M.S.)--University of Missouri--Rolla, 2007. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed December 7, 2007) Includes bibliographical references (p. 28).

We study a generic minimization problem with separable non-convex piecewise linear costs, showing that the linear programming (LP) relaxation of three textbook mixed integer programming formulations each approximates the cost function by its lower convex envelope. We also show a relationship between this result and classical Lagrangian duality theory.

Thesis (Ph. D.)--University of Washington, 2002. / Vita. Includes bibliographical references (leaves 71-75).

Thesis (D.A.)--Illinois State University, 1989. / Title from title page screen, viewed October 14, 2005. Dissertation Committee: Michael J. Plantholt (chair), John A. Dossey, Patricia H. Klass, James T. Parr, Lawrence E. Spence. Includes bibliographical references (leaves 87-89) and abstract. Also available in print.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1981. / Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 117-121).

Optimization plays an important role in many methods routinely used in statistics, machine learning and data science. Often, implementations of these methods rely on highly specialized optimization algorithms, designed to be only applicable within a specific application. However, in many instances recent advances, in particular in the field of convex optimization, make it possible to conveniently and straightforwardly use modern solvers instead with the advantage of enabling broader usage scenarios and thus promoting reusability. This paper introduces the R Optimization Infrastructure which provides an extensible infrastructure to model linear, quadratic, conic and general nonlinear optimization problems in a consistent way. Furthermore, the infrastructure administers many different solvers, reformulations, problem collections and functions to read and write optimization problems in various formats. / Series: Research Report Series / Department of Statistics and Mathematics