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<!-- Header table. Introduction. -->
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'''Welcome to the Cornell University Computational Optimization Open Textbook.''' <br />
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This electronic textbook is a student-contributed open-source text covering a variety of topics on process optimization.
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<br />
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If you have any comments or suggestions on this open textbook, please contact [//https://www.engineering.cornell.edu/faculty-directory/fengqi-you  Professor Fengqi You].
<div style="font-size:162%; border:none; margin:0; padding:.1em; color:#000;">Welcome to the Cornell University Computational Optimization Open Textbook</div>
<br />
----
<br /><br />
<font size="6">Cornell University Open Text Book on Computational Optimization</font>


{| class="wikitable" style="padding: 1em; text-align:left"
This electronic textbook is a student-contributed open-source text covering a variety of topics on process optimization.<br />
|- valign="top"
'''If you have any comments or suggestions on this open textbook, please contact [https://www.engineering.cornell.edu/faculty-directory/fengqi-you  Professor Fengqi You].'''
|width = "400pt"|<br />'''&nbsp;&nbsp;Linear Programming (LP)'''
|}
# [[Duality]]
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# [[Computational complexity]]
# [[Network flow problem]]
# [[Interior-point method for LP]]
# [[Optimization with absolute values]]
# [[Matrix game (LP for game theory)]]
<br />


|width = "400pt"|<br />'''&nbsp;&nbsp;Mixed-Integer Linear Programming (MILP)'''
{| id="mp-upper" style="width: 100%; margin:6px 0 0 0; background:none; border-spacing: 0px;"
# [[Mixed-integer cuts]]
| class="MainPageBG" style="width:50%; border:1px solid #cef2e0; background:#f5fffa; vertical-align:top; color:#000;" |
# [[Disjunctive inequalities]]  
{| id="mp-left" style="width:100%; vertical-align:top; background:#f5fffa;"
# [[Lagrangean duality]]
! style="padding:2px;" | <h2 id="mp-tfa-h2" style="margin:3px; background:#cef2e0; font-size:120%; font-weight:bold; border:1px solid #a3bfb1; text-align:left; color:#000; padding:0.2em 0.4em;">Linear Programming (LP)</h2>
# [[Column generation algorithms]]
|-
# [[Heuristic algorithms]]
| style="color:#000;" | <div id="mp-tfa" style="padding:2px 5px 5px 15px">
# [[Branch and cut]]
      <li>[[Duality]]</li>
# [[Local branching]]
      <li>[[Simplex algorithm]]</li>
# [[Feasibility pump]]
      <li>[[Computational complexity]]</li>
<br />
      <li>[[Network flow problem]]</li>
 
      <li>[[Interior-point method for LP]]</li>
|- valign="top"
      <li>[[Optimization with absolute values]]</li>
|<br />'''&nbsp;&nbsp;NonLinear Programming (NLP)'''
      <li>[[Matrix game (LP for game theory)]]</li>
# [[Line search methods]]  
</div>
# [[Trust-region methods]]  
|-
# [[Interior-point method for NLP]]  
! style="padding:2px" | <h2 id="mp-dyk-h2" style="margin:3px; background:#cef2e0; font-size:120%; font-weight:bold; border:1px solid #a3bfb1; text-align:left; color:#000; padding:0.2em 0.4em;">NonLinear Programming (NLP)</h2>
# [[Conjugate gradient methods]]  
|-
# [[Quasi-Newton methods]]  
| style="color:#000;padding:2px 5px 5px 15px" | <div id="mp-dyk">
# [[Quadratic programming]]
      <li>[[Line search methods]]</li>
# [[Sequential quadratic programming]]
      <li>[[Trust-region methods]]</li>
# [[Subgradient optimization]]
      <li>[[Interior-point method for NLP]]</li>
# [[Mathematical programming with equilibrium constraints]]
      <li>[[Conjugate gradient methods]]</li>
# [[Dynamic optimization]]
      <li>[[Quasi-Newton methods]]</li>
# [[Geometric programming]]
      <li>[[Quadratic programming]]</li>
# [[Nondifferentiable Optimization]]  
      <li>[[Sequential quadratic programming]]</li>
<br />
      <li>[[Subgradient optimization]]</li>
 
      <li>[[Mathematical programming with equilibrium constraints]]</li>
|<br />'''&nbsp;&nbsp;Mixed-Integer NonLinear Programming (MINLP)'''
      <li>[[Dynamic optimization]]</li>
# [[Signomial problems]]
      <li>[[Geometric programming]]</li>
# [[Mixed-integer linear fractional programming (MILFP)]]
      <li>[[Nondifferentiable Optimization]]</li>
# [[Convex Generalized disjunctive programming (GDP)]]
</div>
# [[Nonconvex Generalized disjunctive programming (GDP)]]
|-
# [[Branch and bound (BB) for MINLP]]
! style="padding:2px" | <h2 id="mp-dyk-h2" style="margin:3px; background:#cef2e0; font-size:120%; font-weight:bold; border:1px solid #a3bfb1; text-align:left; color:#000; padding:0.2em 0.4em;">Deterministic Global Optimization</h2>
# [[Branch and cut for MINLP]]
|-
# [[Generalized Benders decomposition (GBD)]]
| style="color:#000;padding:2px 5px 5px 15px" | <div id="mp-dyk">
# [[Outer-approximation (OA)]]
      <li>[[Exponential transformation]]</li>
# [[Extended cutting plane (ECP)]]
      <li>[[Logarithmic transformation]]</li>
<br />  
      <li>[[McCormick envelopes]]</li>
 
      <li>[[Piecewise linear approximation]]</li>
|- valign="top"
      <li>[[Spatial branch and bound method]]</li>
 
</div>
|<br />'''&nbsp;&nbsp; Deterministic Global Optimization'''
|-
# [[Exponential transformation]]
! style="padding:2px" | <h2 id="mp-dyk-h2" style="margin:3px; background:#cef2e0; font-size:120%; font-weight:bold; border:1px solid #a3bfb1; text-align:left; color:#000; padding:0.2em 0.4em;">Dynamic Programming</h2>
# [[Logarithmic transformation]]
|-
# [[McCormick envelopes]]
| style="color:#000;padding:2px 5px 5px 15px" | <div id="mp-dyk">
# [[Piecewise linear approximation]]
      <li>[[Markov decision process]]</li>
# [[Spatial branch and bound method]]
      <li>[[Bellman equation]]</li>
<br />  
      <li>[[Eight step procedures]]</li>
 
      <li>[[Stochastic dynamic programming]]</li>
|<br />'''&nbsp;&nbsp;Optimization under Uncertainty'''
</div>
# [[Stochastic programming]]
|-
# [[Chance-constraint method]]
! style="padding:2px" | <h2 id="mp-dyk-h2" style="margin:3px; background:#cef2e0; font-size:120%; font-weight:bold; border:1px solid #a3bfb1; text-align:left; color:#000; padding:0.2em 0.4em;">Traditional Applications</h2>
# [[Fuzzy programming]]
|-
# [[Classical robust optimization]]
| style="color:#000;padding:2px 5px 5px 15px" | <div id="mp-dyk">
# [[Distributionally robust optimization]]
      <li>[[Facility location problem]]</li>
# [[Adaptive robust optimization]]
      <li>[[Traveling salesman problem]]</li>
# [[Data driven robust optimization]]
      <li>[[Set covering problem]]</li>
<br />
      <li>[[Quadratic assignment problem]]</li>
 
      <li>[[Job shop scheduling]]</li>
 
      <li>[[Newsvendor problem]]</li>
|- valign="top"
      <li>[[Unit commitment problem]]</li>
 
      <li>[[Portfolio optimization]]</li>
 
</div>
|<br />'''&nbsp;&nbsp;Optimization for Machine Learning and Data Analytics'''
# [[Stochastic gradient descent]]
# [[Momentum]]
# [[AdaGrad]]
# [[RMSProp]]
# [[Adam]]
# [[Alternating direction method of multiplier (ADMM)]]
# [[Frank-Wolfe]]
<br />
 
|<br />'''&nbsp;&nbsp;Featured Applications'''
# [[Facility location problem]]  
# [[Traveling salesman problem]]
# [[Portfolio optimization]]  
# [[Set covering problem]]
# [[Unit commitment problem]]
# [[Wing Shape Optimization]]
# [[Optimization in Game Theory]]
<br />


|}


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| class="MainPageBG" style="width:50%; border:1px solid #cedff2; background:#f5faff; vertical-align:top;"|
{| id="mp-right" style="width:100%; vertical-align:top; background:#f5faff;"
! style="padding:2px" | <h2 id="mp-otd-h2" style="margin:3px; background:#cedff2; font-size:120%; font-weight:bold; border:1px solid #a3b0bf; text-align:left; color:#000; padding:0.2em 0.4em;">Mixed-Integer Linear Programming (MILP)</h2>
|-
| style="color:#000;padding:2px 5px 5px 15px" | <div id="mp-otd">
      <li>[[Mixed-integer cuts]]</li>
      <li>[[Disjunctive inequalities]]</li>
      <li>[[Lagrangean duality]]</li>
      <li>[[Column generation algorithms]]</li>
      <li>[[Heuristic algorithms]]</li>
      <li>[[Branch and cut]]</li>
      <li>[[Local branching]]</li></div>
|-
! style="padding:2px" | <h2 id="mp-otd-h2" style="margin:3px; background:#cedff2; font-size:120%; font-weight:bold; border:1px solid #a3b0bf; text-align:left; color:#000; padding:0.2em 0.4em;">Mixed-Integer NonLinear Programming (MINLP)</h2>
|-
| style="color:#000;padding:2px 5px 5px 15px" | <div id="mp-otd">
      <li>[[Signomial problems]]</li>
      <li>[[Mixed-integer linear fractional programming (MILFP)]]</li>
      <li>[[Convex generalized disjunctive programming (GDP)]]</li>
      <li>[[Nonconvex generalized disjunctive programming (GDP)]]</li>
      <li>[[Branch and bound (BB) for MINLP]]</li>
      <li>[[Branch and cut for MINLP]]</li>
      <li>[[Generalized Benders decomposition (GBD)]]</li>
      <li>[[Outer-approximation (OA)]]</li>
      <li>[[Extended cutting plane (ECP)]]</li>
</div>
|-
! style="padding:2px" | <h2 id="mp-otd-h2" style="margin:3px; background:#cedff2; font-size:120%; font-weight:bold; border:1px solid #a3b0bf; text-align:left; color:#000; padding:0.2em 0.4em;">Optimization under Uncertainty</h2>
|-
| style="color:#000;padding:2px 5px 5px 15px" | <div id="mp-dyk">
      <li>[[Stochastic programming]]</li>
      <li>[[Chance-constraint method]]</li>
      <li>[[Fuzzy programming]]</li>
      <li>[[Classical robust optimization]]</li>
      <li>[[Adaptive robust optimization]]</li>
      <li>[[Data driven robust optimization]]</li>
</div>
|-
! style="padding:2px" | <h2 id="mp-otd-h2" style="margin:3px; background:#cedff2; font-size:120%; font-weight:bold; border:1px solid #a3b0bf; text-align:left; color:#000; padding:0.2em 0.4em;">Optimization for Machine Learning and Data Analytics</h2>
|-
| style="color:#000;padding:2px 5px 5px 15px" | <div id="mp-dyk">
      <li>[[Stochastic gradient descent]]</li>
      <li>[[Momentum]]</li>
      <li>[[AdaGrad]]</li>
      <li>[[RMSProp]]</li>
      <li>[[Adam]]</li>
      <li>[[Frank-Wolfe]]</li>
      <li>[[Sparse Reconstruction with Compressed Sensing]]</li>
</div>
|-
! style="padding:2px" | <h2 id="mp-otd-h2" style="margin:3px; background:#cedff2; font-size:120%; font-weight:bold; border:1px solid #a3b0bf; text-align:left; color:#000; padding:0.2em 0.4em;">Emerging Applications</h2>
|-
| style="color:#000;padding:2px 5px 5px 15px" | <div id="mp-dyk">
      <li>[[Wing shape optimization]]</li>
      <li>[[Optimization in game theory]]</li>
      <li>[[Quantum computing for optimization]]</li>
</div>
|}
|}
|}


== Sponsor ==
[[File:Peese-logo.jpg|Cornell Prof. Fengqi You Research Group |link=https://www.peese.org]]


== Getting started ==
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Latest revision as of 20:45, 9 October 2023

Welcome to the Cornell University Computational Optimization Open Textbook

This electronic textbook is a student-contributed open-source text covering a variety of topics on process optimization.
If you have any comments or suggestions on this open textbook, please contact Professor Fengqi You.

Linear Programming (LP)

NonLinear Programming (NLP)

Deterministic Global Optimization

Dynamic Programming

Traditional Applications

Mixed-Integer Linear Programming (MILP)

Mixed-Integer NonLinear Programming (MINLP)

Optimization under Uncertainty

Optimization for Machine Learning and Data Analytics

Emerging Applications

Cornell Prof. Fengqi You Research Group


Retrieved from "https://optimization.cbe.cornell.edu/index.php?title=Main_Page&oldid=6709"