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'''Welcome to the Northwestern University Process 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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{| style="width:100%; border:none; background:none;"
<br />
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| style="text-align:center; white-space:nowrap; color:#000;" |
If you have any comments or suggestions on this open textbook, please contact [//www.orie.cornell.edu/orie/people/field-profile.cfm?netid=fy86_field  Professor Fengqi You].
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<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">Northwestern University Open Text Book on Process Optimization</font>
 
  
{| class="wikitable" style="padding: 1em; text-align:left"
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This electronic textbook is a student-contributed open-source text covering a variety of topics on process optimization.<br />
|- valign="top"
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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].'''
|width = "400pt"|<br />'''&nbsp;&nbsp;Linear Programming (LP)'''
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# [[Computational complexity]]
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|}
# [[Matrix game (LP for game theory)]]
 
# [[Network flow problem]]
 
# [[Interior-point method for LP]]
 
# [[Optimization with absolute values]]
 
<br />
 
  
|width = "400pt"|<br />'''&nbsp;&nbsp;Mixed-Integer Linear Programming (MILP)'''
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{| id="mp-upper" style="width: 100%; margin:6px 0 0 0; background:none; border-spacing: 0px;"
# [[Facility location problems]]
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| class="MainPageBG" style="width:50%; border:1px solid #cef2e0; background:#f5fffa; vertical-align:top; color:#000;" |
# [[Traveling salesman problems]]  
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{| id="mp-left" style="width:100%; vertical-align:top; background:#f5fffa;"
# [[Mixed-integer cuts]]  
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! 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>
# [[Disjunctive inequalities]]  
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|-
# [[Lagrangean duality]]
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| style="color:#000;" | <div id="mp-tfa" style="padding:2px 5px">
# [[Column generation algorithms]]
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      <li>[[Duality]]</li>
# [[Heuristic algorithms]]
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      <li>[[Simplex algorithm]]</li>
# [[Branch and cut]]
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      <li>[[Computational complexity]]</li>
<br />
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      <li>[[Network flow problem]]</li>
 
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      <li>[[Interior-point method for LP]]</li>
|- valign="top"
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      <li>[[Optimization with absolute values]]</li>
|<br />'''&nbsp;&nbsp;NonLinear Programming (NLP)'''
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      <li>[[Matrix game (LP for game theory)]]</li>
# [[Line search methods]]  
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</div>
# [[Trust-region methods]]  
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|-
# [[Interior-point method for NLP]]  
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! 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]]  
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|-
# [[Quasi-Newton methods]]  
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| style="color:#000;padding:2px 5px 5px" | <div id="mp-dyk">
# [[Quadratic programming]]
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      <li>[[Line search methods]]</li>
# [[Sequential quadratic programming]]
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      <li>[[Trust-region methods]]</li>
# [[Subgradient optimization]]
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      <li>[[Interior-point method for NLP]]</li>
# [[Mathematical programming with equilibrium constraints]]
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      <li>[[Conjugate gradient methods]]</li>
# [[Dynamic optimization]]
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      <li>[[Quasi-Newton methods]]</li>
# [[Geometric programming]]
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      <li>[[Quadratic programming]]</li>
# [[Nondifferentiable Optimization]]  
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      <li>[[Sequential quadratic programming]]</li>
<br />
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      <li>[[Subgradient optimization]]</li>
 
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      <li>[[Mathematical programming with equilibrium constraints]]</li>
|<br />'''&nbsp;&nbsp;Mixed-Integer NonLinear Programming (MINLP)'''
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      <li>[[Dynamic optimization]]</li>
# [[Signomial problems]]
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      <li>[[Geometric programming]]</li>
# [[Mixed-integer linear fractional programming (MILFP)]]
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      <li>[[Nondifferentiable Optimization]]</li>
# [[Convex Generalized disjunctive programming (GDP)]]
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</div>
# [[Nonconvex Generalized disjunctive programming (GDP)]]
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|-
# [[Branch and bound (BB)]]
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! 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]]
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|-
# [[Generalized Benders decomposition (GBD)]]
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| style="color:#000;padding:2px 5px 5px" | <div id="mp-dyk">
# [[Outer-approximation (OA)]]
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      <li>[[Exponential transformation]]</li>
# [[Extended cutting plane (ECP)]]
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      <li>[[Logarithmic transformation]]</li>
<br />  
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      <li>[[McCormick envelopes]]</li>
 
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      <li>[[Piecewise linear approximation]]</li>
|- valign="top"
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      <li>[[Spatial branch and bound method]]</li>
 
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</div>
|<br />'''&nbsp;&nbsp;Global Optimization'''
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|-
# [[Exponential transformation]]
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! 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]]
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|-
# [[McCormick envelopes]]
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| style="color:#000;padding:2px 5px 5px" | <div id="mp-dyk">
# [[Piecewise linear approximation]]
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      <li>[[Markov decision process]]</li>
# [[Spatial branch and bound method]]
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      <li>[[Bellman equation]]</li>
<br />  
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      <li>[[Eight step procedures]]</li>
 
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      <li>[[Stochastic dynamic programming]]</li>
|<br />'''&nbsp;&nbsp;Optimization under Uncertainty'''
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</div>
# [[Stochastic programming]]
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|-
# [[Chance-constraint method]]
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! 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]]
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|-
# [[Classical robust optimization]]
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| style="color:#000;padding:2px 5px 5px" | <div id="mp-dyk">
# [[Adaptive robust optimization]]
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      <li>[[Facility location problem]]</li>
# [[Data driven robust optimization]]
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      <li>[[Traveling salesman problem]]</li>
<br />
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      <li>[[Set covering problem]]</li>
 
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      <li>[[Quadratic assignment problem]]</li>
 
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      <li>[[Newsvendor problem]]</li>  
|- valign="top"
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      <li>[[Unit commitment problem]]</li>
 
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      <li>[[Portfolio optimization]]</li>
|<br />'''&nbsp;&nbsp;Featured Applications'''
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</div>
# [[Wing Shape Optimization]]
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|}
# [[Applying Optimization in Game Theory]]
 
<br />
 
  
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<!--        IN THE NEWS; ON THIS DAY        -->
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| class="MainPageBG" style="width:50%; border:1px solid #cedff2; background:#f5faff; vertical-align:top;"|
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{| id="mp-right" style="width:100%; vertical-align:top; background:#f5faff;"
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! 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>
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|-
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| style="color:#000;padding:2px 5px 5px" | <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>
 +
      <li>[[Feasibility pump]]</li>
 +
</div>
 +
|-
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! 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>
 +
|-
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| style="color:#000;padding:2px 5px 5px" | <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" | <div id="mp-dyk">
 +
      <li>[[Stochastic programming]]</li>
 +
      <li>[[Chance-constraint method]]</li>
 +
      <li>[[Fuzzy programming]]</li>
 +
      <li>[[Classical robust optimization]]</li>
 +
      <li>[[Distributionally 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" | <div id="mp-dyk">
 +
      <li>[[Stochastic gradient descent]]</li>
 +
      <li>[[Momentum]]</li>
 +
      <li>[[AdaGrad]]</li>
 +
      <li>[[RMSProp]]</li>
 +
      <li>[[Adam]]</li>
 +
      <li>[[Alternating direction method of multiplier (ADMM)]]</li>
 +
      <li>[[Frank-Wolfe]]</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>
 +
|-
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| style="color:#000;padding:2px 5px 5px" | <div id="mp-dyk">
 +
      <li>[[Protein folding problem]]</li>
 +
      <li>[[Wing shape optimization]]</li>
 +
      <li>[[Optimization in game theory]]</li>
 +
      <li>[[Quantum computing for optimization]]</li>
 +
</div>
 +
|}
 
|}
 
|}
  
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== Sponsor ==
 +
[[File:Peese-logo.jpg|Cornell Prof. Fengqi You Research Group |link=https://www.peese.org]]
  
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Latest revision as of 18:06, 17 November 2020

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