Document Type


Date of Degree

Fall 2009

Degree Name

PhD (Doctor of Philosophy)

Degree In

Industrial Engineering

First Advisor

Pavlo Krokhmal

First Committee Member

Yong Chen

Second Committee Member

Peter O'Grady

Third Committee Member

Andrew Kusiak

Fourth Committee Member

Samuel Burer


My dissertation considers solving of linear programming problems with p-order conic constraints that are related to a class of stochastic optimization models with risk objective or constraints that involve higher moments of loss distributions. The general proposed approach is based on construction of polyhedral approximations for p-order cones, thereby approximating the non-linear convex p-order conic programming problems using linear programming models. It is shown that the resulting LP problems possess a special structure that makes them amenable to efficient decomposition techniques. The developed algorithms are tested on the example of portfolio optimization problem with higher moment coherent risk measures that reduces to a p-order conic programming problem. The conducted case studies on real financial data demonstrate that the proposed computational techniques compare favorably against a number of benchmark methods, including second-order conic programming methods.


cutting plane, decomposition algorithm, Higher Moment Risk Models, p-order conic constraint, Portfolio optimization, Stochastic optimization


x, 122 pages


Includes bibliographical references (pages 119-122).


Copyright 2009 Policarpio Antonio Soberanis