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<!-- Header table. Introduction. -->
{| id="mp-topbanner" style="width:100%; background:#f6f6f6; margin-top:1.2em; border:1px solid #ddd;"
'''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.
{| style="width:100%; border:none; background:none;"
<br />
| style="text-align:center; white-space:nowrap; color:#000;" |
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 Open Textbook 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]]
|}
# [[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>
      <li>[[Optimization with absolute values]]</li>
      <li>[[Matrix game (LP for game theory)]]</li>
</div>
|-
! 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>
|-
| style="color:#000;padding:2px 5px 5px 15px" | <div id="mp-dyk">
      <li>[[Line search methods]]</li>
      <li>[[Trust-region methods]]</li>
      <li>[[Interior-point method for NLP]]</li>
      <li>[[Conjugate gradient methods]]</li>
      <li>[[Quasi-Newton methods]]</li>
      <li>[[Quadratic programming]]</li>
      <li>[[Sequential quadratic programming]]</li>
      <li>[[Subgradient optimization]]</li>
      <li>[[Mathematical programming with equilibrium constraints]]</li>
      <li>[[Dynamic optimization]]</li>
      <li>[[Geometric programming]]</li>
      <li>[[Nondifferentiable Optimization]]</li>
</div>
|-
! 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>
|-
| style="color:#000;padding:2px 5px 5px 15px" | <div id="mp-dyk">
      <li>[[Exponential transformation]]</li>
      <li>[[Logarithmic transformation]]</li>
      <li>[[McCormick envelopes]]</li>
      <li>[[Piecewise linear approximation]]</li>
      <li>[[Spatial branch and bound method]]</li>
</div>
|-
! 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>
|-
| style="color:#000;padding:2px 5px 5px 15px" | <div id="mp-dyk">
      <li>[[Markov decision process]]</li>
      <li>[[Bellman equation]]</li>
      <li>[[Eight step procedures]]</li>
      <li>[[Stochastic dynamic programming]]</li>
</div>
|-
! 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>
|-
| style="color:#000;padding:2px 5px 5px 15px" | <div id="mp-dyk">
      <li>[[Facility location problem]]</li>
      <li>[[Traveling salesman problem]]</li>
      <li>[[Set covering problem]]</li>
      <li>[[Quadratic assignment problem]]</li>
      <li>[[Job shop scheduling]]</li>
      <li>[[Newsvendor problem]]</li>
      <li>[[Unit commitment problem]]</li>
      <li>[[Portfolio optimization]]</li>
</div>


|- valign="top"
|}
|<br />'''&nbsp;&nbsp;NonLinear Programming (NLP)'''
# [[Line search methods]]
# [[Trust-region methods]]
# [[Interior-point method for NLP]]
# [[Conjugate gradient methods]]
# [[Quasi-Newton methods]]
# [[Quadratic programming]]
# [[Sequential quadratic programming]]
# [[Subgradient optimization]]
# [[Mathematical programming with equilibrium constraints]]
# [[Dynamic optimization]]
# [[Geometric programming]]
# [[Nondifferentiable Optimization]]
<br />


|<br />'''&nbsp;&nbsp;Mixed-Integer NonLinear Programming (MINLP)'''
| style="border:1px solid transparent;" |
# [[Signomial problems]]
| class="MainPageBG" style="width:50%; border:1px solid #cedff2; background:#f5faff; vertical-align:top;"|
# [[Mixed-integer linear fractional programming (MILFP)]]
{| id="mp-right" style="width:100%; vertical-align:top; background:#f5faff;"
# [[Convex Generalized disjunctive programming (GDP)]]
! 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>
# [[Nonconvex Generalized disjunctive programming (GDP)]]
|-
# [[Branch and bound (BB) for MINLP]]
| style="color:#000;padding:2px 5px 5px 15px" | <div id="mp-otd">
# [[Branch and cut for MINLP]]
      <li>[[Mixed-integer cuts]]</li>
# [[Generalized Benders decomposition (GBD)]]
      <li>[[Disjunctive inequalities]]</li>
# [[Outer-approximation (OA)]]
      <li>[[Lagrangean duality]]</li>
# [[Extended cutting plane (ECP)]]
      <li>[[Column generation algorithms]]</li>
<br />  
      <li>[[Heuristic algorithms]]</li>
 
      <li>[[Branch and cut]]</li>
|- valign="top"
      <li>[[Local branching]]</li></div>
 
|-
|<br />'''&nbsp;&nbsp; Deterministic Global Optimization'''
! 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>
# [[Exponential transformation]]
|-
# [[Logarithmic transformation]]
| style="color:#000;padding:2px 5px 5px 15px" | <div id="mp-otd">
# [[McCormick envelopes]]
      <li>[[Signomial problems]]</li>
# [[Piecewise linear approximation]]
      <li>[[Mixed-integer linear fractional programming (MILFP)]]</li>
# [[Spatial branch and bound method]]
      <li>[[Convex generalized disjunctive programming (GDP)]]</li>
<br />  
      <li>[[Nonconvex generalized disjunctive programming (GDP)]]</li>
 
      <li>[[Branch and bound (BB) for MINLP]]</li>
|<br />'''&nbsp;&nbsp;Optimization under Uncertainty'''
      <li>[[Branch and cut for MINLP]]</li>
# [[Stochastic programming]]  
      <li>[[Generalized Benders decomposition (GBD)]]</li>
# [[Chance-constraint method]]
      <li>[[Outer-approximation (OA)]]</li>
# [[Fuzzy programming]]
      <li>[[Extended cutting plane (ECP)]]</li>
# [[Classical robust optimization]]
</div>
# [[Distributionally robust optimization]]
|-
# [[Adaptive robust optimization]]
! 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>
# [[Data driven robust optimization]]
|-
<br />
| style="color:#000;padding:2px 5px 5px 15px" | <div id="mp-dyk">
 
      <li>[[Stochastic programming]]</li>
 
      <li>[[Chance-constraint method]]</li>
|- valign="top"
      <li>[[Fuzzy programming]]</li>
 
      <li>[[Classical robust optimization]]</li>
|<br />'''&nbsp;&nbsp;Dynamic Programming'''
      <li>[[Adaptive robust optimization]]</li>
# [[Markov decision process]]
      <li>[[Data driven robust optimization]]</li>
# [[Bellman equation]]
</div>
# [[Eight step procedures]]
|-
# [[Stochastic dynamic programming]]
! 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>
<br />
|-
 
| style="color:#000;padding:2px 5px 5px 15px" | <div id="mp-dyk">
|<br />'''&nbsp;&nbsp;Optimization for Machine Learning and Data Analytics'''
      <li>[[Stochastic gradient descent]]</li>
# [[Stochastic gradient descent]]  
      <li>[[Momentum]]</li>
# [[Momentum]]
      <li>[[AdaGrad]]</li>
# [[AdaGrad]]
      <li>[[RMSProp]]</li>
# [[RMSProp]]
      <li>[[Adam]]</li>
# [[Adam]]
      <li>[[Frank-Wolfe]]</li>
# [[Alternating direction method of multiplier (ADMM)]]
      <li>[[Sparse Reconstruction with Compressed Sensing]]</li>
# [[Frank-Wolfe]]
</div>
<br />
|-
 
! 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">
|- valign="top"
      <li>[[Wing shape optimization]]</li>
 
      <li>[[Optimization in game theory]]</li>
 
      <li>[[Quantum computing for optimization]]</li>
|<br />'''&nbsp;&nbsp;Traditional Applications'''
</div>
# [[Facility location problem]]
|}
# [[Traveling salesman problem]]
# [[Portfolio optimization]]
# [[Set covering problem]]
# [[Unit commitment problem]]
# [[Quadratic assignment problem]]
<br />
 
|<br />'''&nbsp;&nbsp;Emerging Applications'''
# [[Protein folding problem]]
# [[Wing Shape Optimization]]
# [[Optimization in Game Theory]]
# [[Quantum computing for optimization]]
<br />
|}
|}


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


== Link ==
</noinclude>__NOTOC____NOEDITSECTION__
[[File:Peese-logo.jpg|120px|Cornell PEESE Group |link=https://www.peese.org]]

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"