<p> In this thesis parametric analysis for conic quadratic optimization problems
is studied. In parametric analysis, which is often referred to as parametric optimization
or parametric programming, a perturbation parameter is introduced
into the optimization problem, which means that the coefficients in the objective
function of the problem and in the right-hand-side of the constraints are
perturbed. First, we describe linear, convex quadratic and second order cone optimization
problems and their parametric versions. Second, the theory for finding
solutions of the parametric problems is developed. We also present algorithms
for solving such problems. Third, we demonstrate how to use parametric optimization
techniques to solve multiobjective optimization problems and compute
Pareto efficient surfaces. </p> <p> We implement our novel algorithm for hi-parametric quadratic optimization.
It utilizes existing solvers to solve auxiliary problems. We present numerical
results produced by our parametric optimization package on a number of practical
financial and non-financial computational problems. In the latter we consider
problems of drug design and beam intensity optimization for radiation therapy. </p> <p> In the financial applications part, two risk management optimization models
are developed or extended. These two models are a portfolio replication
framework and a credit risk optimization framework. We describe applications
of multiobjective optimization to existing financial models and novel models that
we have developed. We solve a number of examples of financial multiobjective
optimization problems using our parametric optimization algorithms. </p> / Thesis / Doctor of Philosophy (PhD)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/19370 |
| Date | 03 1900 |
| Creators | Romanko, Oleksandr |
| Contributors | Terlaky, Tamas, Deza, Antoine, Computing and Software |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
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