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<!-- Header table. Introduction. -->
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{| id="mp-topbanner" style="width:100%; background:#f6f6f6; margin-top:1.2em; border:1px solid #ddd;"
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'''Welcome to the Cornell University Computational Optimization Open Textbook.''' <br />
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| style="width:61%; color:#000;" |
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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;"
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<br />
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| style="text-align:center; white-space:nowrap; color:#000;" |
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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].
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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>
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<br />
 
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----
 
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<br /><br />
 
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<font size="6">Cornell Open Textbook on Computational Optimization</font>
 
  
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{| 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 />
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|- 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].'''
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|width = "400pt"|<br />'''&nbsp;&nbsp;Linear Programming (LP)'''
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|}
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# [[Duality]]
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|}
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# [[Computational complexity]]
 
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# [[Network flow problem]]
 
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# [[Interior-point method for LP]]
 
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# [[Optimization with absolute values]]
 
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# [[Matrix game (LP for game theory)]]
 
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<br />
 
  
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|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;"
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# [[Mixed-integer cuts]]  
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| class="MainPageBG" style="width:50%; border:1px solid #cef2e0; background:#f5fffa; vertical-align:top; color:#000;" |
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# [[Disjunctive inequalities]]  
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{| id="mp-left" style="width:100%; vertical-align:top; background:#f5fffa;"
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# [[Lagrangean duality]]
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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>
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# [[Column generation algorithms]]
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|-
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# [[Heuristic algorithms]]
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| style="color:#000;" | <div id="mp-tfa" style="padding:2px 5px">
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# [[Branch and cut]]
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      <li>[[Duality]]</li>
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# [[Local branching]]
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      <li>[[Simplex algorithm]]</li>
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# [[Feasibility pump]]
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      <li>[[Computational complexity]]</li>
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<br />
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      <li>[[Network flow problem]]</li>
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      <li>[[Interior-point method for LP]]</li>
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      <li>[[Optimization with absolute values]]</li>
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      <li>[[Matrix game (LP for game theory)]]</li>
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</div>
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|-
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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>
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|-
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| style="color:#000;padding:2px 5px 5px" | <div id="mp-dyk">
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      <li>[[Line search methods]]</li>
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      <li>[[Trust-region methods]]</li>
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      <li>[[Interior-point method for NLP]]</li>
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      <li>[[Conjugate gradient methods]]</li>
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      <li>[[Quasi-Newton methods]]</li>
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      <li>[[Quadratic programming]]</li>
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      <li>[[Sequential quadratic programming]]</li>
 +
      <li>[[Subgradient optimization]]</li>
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      <li>[[Mathematical programming with equilibrium constraints]]</li>
 +
      <li>[[Dynamic optimization]]</li>
 +
      <li>[[Geometric programming]]</li>
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      <li>[[Nondifferentiable Optimization]]</li>
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</div>
 +
|-
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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>
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|-
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| style="color:#000;padding:2px 5px 5px" | <div id="mp-dyk">
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      <li>[[Exponential transformation]]</li>
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      <li>[[Logarithmic transformation]]</li>
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      <li>[[McCormick envelopes]]</li>
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      <li>[[Piecewise linear approximation]]</li>
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      <li>[[Spatial branch and bound method]]</li>
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</div>
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|-
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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>
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|-
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| style="color:#000;padding:2px 5px 5px" | <div id="mp-dyk">
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      <li>[[Markov decision process]]</li>
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      <li>[[Bellman equation]]</li>
 +
      <li>[[Eight step procedures]]</li>
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      <li>[[Stochastic dynamic programming]]</li>
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</div>
 +
|-
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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>
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|-
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| style="color:#000;padding:2px 5px 5px" | <div id="mp-dyk">
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      <li>[[Facility location problem]]</li>
 +
      <li>[[Traveling salesman problem]]</li>
 +
      <li>[[Set covering problem]]</li>
 +
      <li>[[Quadratic assignment problem]]</li>
 +
      <li>[[Newsvendor problem]]</li>
 +
      <li>[[Unit commitment problem]]</li>
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      <li>[[Portfolio optimization]]</li>
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</div>
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|}
  
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|- valign="top"
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| style="border:1px solid transparent;" |
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|<br />'''&nbsp;&nbsp;NonLinear Programming (NLP)'''
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<!--        IN THE NEWS; ON THIS DAY        -->
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# [[Line search methods]]
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| class="MainPageBG" style="width:50%; border:1px solid #cedff2; background:#f5faff; vertical-align:top;"|
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# [[Trust-region methods]]
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{| id="mp-right" style="width:100%; vertical-align:top; background:#f5faff;"
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# [[Interior-point method for NLP]]
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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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# [[Conjugate gradient methods]]
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|-
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# [[Quasi-Newton methods]]  
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| style="color:#000;padding:2px 5px 5px" | <div id="mp-otd">
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# [[Quadratic programming]]
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      <li>[[Mixed-integer cuts]]</li>
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# [[Sequential quadratic programming]]
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      <li>[[Disjunctive inequalities]]</li>
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# [[Subgradient optimization]]
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      <li>[[Lagrangean duality]]</li>
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# [[Mathematical programming with equilibrium constraints]]
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      <li>[[Column generation algorithms]]</li>
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# [[Dynamic optimization]]
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      <li>[[Heuristic algorithms]]</li>
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# [[Geometric programming]]
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      <li>[[Branch and cut]]</li>
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# [[Nondifferentiable Optimization]]  
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      <li>[[Local branching]]</li>
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<br />
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      <li>[[Feasibility pump]]</li>
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</div>
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|<br />'''&nbsp;&nbsp;Mixed-Integer NonLinear Programming (MINLP)'''
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|-
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# [[Signomial problems]]
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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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# [[Mixed-integer linear fractional programming (MILFP)]]
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|-
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# [[Convex Generalized disjunctive programming (GDP)]]
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| style="color:#000;padding:2px 5px 5px" | <div id="mp-otd">
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# [[Nonconvex Generalized disjunctive programming (GDP)]]
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      <li>[[Signomial problems]]</li>
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# [[Branch and bound (BB) for MINLP]]
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      <li>[[Mixed-integer linear fractional programming (MILFP)]]</li>
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# [[Branch and cut for MINLP]]
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      <li>[[Convex generalized disjunctive programming (GDP)]]</li>
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# [[Generalized Benders decomposition (GBD)]]
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      <li>[[Nonconvex generalized disjunctive programming (GDP)]]</li>
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# [[Outer-approximation (OA)]]
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      <li>[[Branch and bound (BB) for MINLP]]</li>
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# [[Extended cutting plane (ECP)]]
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      <li>[[Branch and cut for MINLP]]</li>
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<br />  
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      <li>[[Generalized Benders decomposition (GBD)]]</li>
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      <li>[[Outer-approximation (OA)]]</li>
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|- valign="top"
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      <li>[[Extended cutting plane (ECP)]]</li>
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</div>
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|<br />'''&nbsp;&nbsp; Deterministic Global Optimization'''
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|-
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# [[Exponential transformation]]
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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;">Optimization under Uncertainty</h2>
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# [[Logarithmic transformation]]
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|-
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# [[McCormick envelopes]]
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| style="color:#000;padding:2px 5px 5px" | <div id="mp-dyk">
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# [[Piecewise linear approximation]]
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      <li>[[Stochastic programming]]</li>
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# [[Spatial branch and bound method]]
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      <li>[[Chance-constraint method]]</li>
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<br />  
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      <li>[[Fuzzy programming]]</li>
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      <li>[[Classical robust optimization]]</li>
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|<br />'''&nbsp;&nbsp;Optimization under Uncertainty'''
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      <li>[[Distributionally robust optimization]]</li>
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# [[Stochastic programming]]  
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      <li>[[Adaptive robust optimization]]</li>
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# [[Chance-constraint method]]
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      <li>[[Data driven robust optimization]]</li>
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# [[Fuzzy programming]]
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</div>
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# [[Classical robust optimization]]
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|-
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# [[Distributionally robust optimization]]
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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;">Optimization for Machine Learning and Data Analytics</h2>
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# [[Adaptive robust optimization]]
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|-
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# [[Data driven robust optimization]]
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| style="color:#000;padding:2px 5px 5px" | <div id="mp-dyk">
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<br />
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      <li>[[Stochastic gradient descent]]</li>
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      <li>[[Momentum]]</li>
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      <li>[[AdaGrad]]</li>
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|- valign="top"
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      <li>[[RMSProp]]</li>
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      <li>[[Adam]]</li>
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|<br />'''&nbsp;&nbsp;Dynamic Programming'''
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      <li>[[Alternating direction method of multiplier (ADMM)]]</li>
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# [[Markov decision process]]
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      <li>[[Frank-Wolfe]]</li>
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# [[Bellman equation]]
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</div>
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# [[Eight step procedures]]
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|-
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# [[Stochastic dynamic programming]]
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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;">Emerging Applications</h2>
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<br />
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|-
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| style="color:#000;padding:2px 5px 5px" | <div id="mp-dyk">
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|<br />'''&nbsp;&nbsp;Optimization for Machine Learning and Data Analytics'''
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      <li>[[Protein folding problem]]</li>
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# [[Stochastic gradient descent]]  
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      <li>[[Wing shape optimization]]</li>
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# [[Momentum]]
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      <li>[[Optimization in game theory]]</li>
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# [[AdaGrad]]
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      <li>[[Quantum computing for optimization]]</li>
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# [[RMSProp]]
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</div>
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# [[Adam]]
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|}
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# [[Alternating direction method of multiplier (ADMM)]]
 
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# [[Frank-Wolfe]]
 
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<br />
 
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|- valign="top"
 
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|<br />'''&nbsp;&nbsp;Traditional Applications'''
 
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# [[Facility location problem]]
 
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# [[Traveling salesman problem]]
 
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# [[Portfolio optimization]]
 
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# [[Set covering problem]]
 
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# [[Unit commitment problem]]
 
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# [[Quadratic assignment problem]]
 
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<br />
 
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|<br />'''&nbsp;&nbsp;Emerging Applications'''
 
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# [[Protein folding problem]]
 
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# [[Wing Shape Optimization]]
 
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# [[Optimization in Game Theory]]
 
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# [[Quantum computing for optimization]]
 
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<br />
 
 
|}
 
|}
  
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== Sponsor ==
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[[File:Peese-logo.jpg|Cornell Prof. Fengqi You Research Group |link=https://www.peese.org]]
  
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== Link ==
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</noinclude>__NOTOC____NOEDITSECTION__
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[[File:Peese-logo.jpg|120px|Cornell Prof. Fengqi You Research Group |link=https://www.peese.org]]
 

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


Retrieved from "https://optimization.cbe.cornell.edu/index.php?title=Main_Page&oldid=1116"