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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.
{| 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 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)'''
|}
# [[Computational complexity]]
|}
# [[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)'''
{| id="mp-upper" style="width: 100%; margin:6px 0 0 0; background:none; border-spacing: 0px;"
# [[Facility location problems]]  
| class="MainPageBG" style="width:50%; border:1px solid #cef2e0; background:#f5fffa; vertical-align:top; color:#000;" |
# [[Traveling salesman problems]]  
{| id="mp-left" style="width:100%; vertical-align:top; background:#f5fffa;"
# [[Mixed-integer cuts]]  
! 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]]  
|-
# [[Lagrangean duality]]
| style="color:#000;" | <div id="mp-tfa" style="padding:2px 5px 5px 15px">
# [[Column generation algorithms]]
      <li>[[Duality]]</li>
# [[Heuristic algorithms]]
      <li>[[Simplex algorithm]]</li>
# [[Branch and cut]]
      <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>
      <li>[[Evolutionary multimodal optimization]]</li>
      <li>[[Stackelberg leadership model]]</li>
      <li>[[Quadratic constrained quadratic programming]]</li>
      <li>[[Derivative free 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>
      <li>[[A-star algorithm]]</li>
</div>


|- valign="top"
|-
|<br />'''&nbsp;&nbsp;NonLinear Programming (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;"> Emerging Applications</h2>
# [[Line search methods]]
|-
# [[Trust-region methods]]
| style="color:#000;padding:2px 5px 5px 15px" | <div id="mp-dyk">
# [[Interior-point method for NLP]]
      <li>[[Wing shape optimization]]</li>
# [[Conjugate gradient methods]]
      <li>[[Optimization in game theory]]</li>
# [[Quasi-Newton methods]]
      <li>[[Quantum computing for optimization]]</li>
# [[Quadratic programming]]
</div>
# [[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)'''
# [[Signomial problems]]
# [[Mixed-integer linear fractional programming (MILFP)]]
# [[Convex Generalized disjunctive programming (GDP)]]
# [[Nonconvex Generalized disjunctive programming (GDP)]]
# [[Branch and bound (BB)]]
# [[Branch and cut for MINLP]]
# [[Generalized Benders decomposition (GBD)]]
# [[Outer-approximation (OA)]]
# [[Extended cutting plane (ECP)]]
<br />
 
|- valign="top"
 
|<br />'''&nbsp;&nbsp;Global Optimization'''
# [[Exponential transformation]]
# [[Logarithmic transformation]]
# [[McCormick envelopes]]
# [[Piecewise linear approximation]]
# [[Spatial branch and bound method]]
<br />  
 
|<br />'''&nbsp;&nbsp;Optimization under Uncertainty'''
# [[Stochastic programming]]
# [[Chance-constraint method]]
# [[Fuzzy programming]]
# [[Classical robust optimization]]
# [[Adaptive robust optimization]]
# [[Data driven robust optimization]]
<br />
 
 
|- valign="top"
 
 
|<br />'''&nbsp;&nbsp;Optimization for Machine Learning and Data Analytics'''
# [[Stochastic gradient descent]]  
# [[Moment]]
# [[RMSProp]]
# [[ADAM]]
<br />
 
|<br />'''&nbsp;&nbsp;Featured Applications'''
# [[Wing Shape Optimization]]
# [[Applying Optimization in Game Theory]]
<br />


|}


| style="border:1px solid transparent;" |
| 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>
      <li>[[Adadelta]]</li>
      <li>[[Adafactor]]</li>
      <li>[[AdamW]]</li>
      <li>[[Adamax]]</li>
      <li>[[FTRL algorithm]]</li>
      <li>[[Lion algorithm]]</li>
      <li>[[LossScaleOptimizer]]</li>
      <li>[[Nadam]]</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;">Black-box Optimization</h2>
|-
| style="color:#000;padding:2px 5px 5px 15px" | <div id="mp-dyk">
      <li>[[Bayesian optimization]]</li>
      <li>[[Genetic algorithm]]</li>
      <li>[[Simulated annealing]]</li>
      <li>[[Particle swarm optimization]]</li>
      <li>[[Differential evolution]]</li>
</div>
|}
|}
|}


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


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Latest revision as of 18:35, 15 December 2024

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

Emerging Applications

Mixed-Integer Linear Programming (MILP)

Mixed-Integer NonLinear Programming (MINLP)

Optimization under Uncertainty

Optimization for Machine Learning and Data Analytics

Black-box Optimization

Cornell Prof. Fengqi You Research Group


Retrieved from "https://optimization.cbe.cornell.edu/index.php?title=Main_Page&oldid=7647"