Optimization Toolbox

<h2 id="optimization-algorithms">Optimization algorithms</h2>
<p>Optimization Toolbox has algorithms for:
</p>
<ul><li><a href="/facts/Linear_programming/GduXFQxT">Linear programming</a></li>
<li><a href="/facts/Integer_programming/MDaaadoA">Mixed-integer linear programming</a></li>
<li><a href="/facts/Quadratic_programming/ct4RIUgs">Quadratic programming</a></li>
<li><a href="/facts/Nonlinear_programming/cSXGuX2m">Nonlinear programming</a></li>
<li><a href="/facts/Linear_least_squares_(mathematics)/dKctFUCV">Linear least squares</a></li>
<li><a href="/facts/Non-linear_least_squares/3K5Nmz0S">Nonlinear least squares</a></li>
<li>Nonlinear equation solving</li>
<li><a href="/facts/Multi-objective_optimization/1Hb4gjGJ">Multi-objective optimization</a></li></ul>
<h2 id="applications">Applications</h2>
<h3>Engineering Optimization</h3>
<p>Optimization Toolbox solvers are used for engineering applications in MATLAB, such as <a href="/facts/Optimal_control/9SmcQHjJ">optimal control</a> and optimal mechanical designs.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a><a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a>
</p>
<h3>Parameter Estimation</h3>
<p>Optimization can help with fitting a model to data, where the goal is to identify the model parameters that minimize the difference between simulated and experimental data. Common parameter estimation problems that are solved with Optimization Toolbox include estimating material parameters and estimating coefficients of <a href="/facts/Ordinary_differential_equations/ygKGQ8kD">ordinary differential equations</a>.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a><a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a>
</p>
<h3>Computational Finance</h3>
<p><a href="/facts/Portfolio_optimization/H1rvkwzX">Portfolio optimization</a>, <a href="/facts/Cashflow_matching/byweBl3M">cashflow matching</a>, and other computational finance problems are solved with Optimization Toolbox.<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a>
</p>
<h3>Utilities and Energy</h3>
<p>Optimization Toolbox solvers are used for security constrained optimal power flow and power systems analysis.<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a>
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Mathematical_optimization/oRn8Iv5I">Mathematical optimization</a></li></ul>

<h2 id="further-reading">Further reading</h2>
<ul><li>Venkataraman, P. (2009). <a href="https://books.google.com/books?id=kKWs51HLLA8C&pg=PA469">"Optimization Toolbox from Matlab"</a>. <i>Applied Optimization with MATLAB Programming</i> (2nd ed.). Hoboken: John Wiley & Sons. pp. 469–488. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-470-08488-5.</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Dragain, Andreas (2009). "Comparative Study of Numerical Methods for Optimal Control of a Biomechanical System" (PDF). Chalmers University of Technology. Retrieved 2013-07-01. <a href="http://publications.lib.chalmers.se/records/fulltext/134033.pdf" target="_blank">http://publications.lib.chalmers.se/records/fulltext/134033.pdf</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Rao, Singiresu (2009). Engineering Optimization: Theory and Practice. Hoboken, New Jersey: John Wiley & Sons. p. 36. ISBN 978-0-470-18352-6. <a href="978-0-470-18352-6" target="_blank">978-0-470-18352-6</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Banks, H.T.; et al. (2013). "Material parameter estimation and hypothesis testing on a 1D viscoelastic stenosis model: Methodology". Journal of Inverse and Ill-Posed Problems. 21 (1): 25–57. doi:10.1515/jip-2012-0081. <a href="http://www.lib.ncsu.edu/resolver/1840.4/8209" target="_blank">http://www.lib.ncsu.edu/resolver/1840.4/8209</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Collins Licata, A.; et al. (2001). "A Physiologically Based Pharmacokinetic Model for Methyl tert-Butyl Ether in Humans: Implementing Sensitivity and Variability Analyses". Toxicological Sciences. 62 (2): 191–204. doi:10.1093/toxsci/62.2.191. PMID 11452131. <a href="https://doi.org/10.1093%2Ftoxsci%2F62.2.191" target="_blank">https://doi.org/10.1093%2Ftoxsci%2F62.2.191</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>Pachamanova, D. (2010). Simulation and Optimization in Finance + Web Site. Hoboken, New Jersey: John Wiley & Sons. ISBN 978-0-470-37189-3. <a href="978-0-470-37189-3" target="_blank">978-0-470-37189-3</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>Cartina, G.; et al. (2007). "Power System Analysis using MATLAB Toolboxes". 6th International Conference on Electromechanical and Power Systems: 305–308. <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
</ol>

Optimization Toolbox open-in-new

Optimization Toolbox