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| {| id="mp-topbanner" style="width:100%; background:#f6f6f6; margin-top:1.2em; border:1px solid #ddd;"
| | <!-- Header table. Introduction. --> |
| | style="width:61%; color:#000;" |
| | '''Welcome to the Cornell University Computational Optimization Open Textbook.''' <br /> |
| {| style="width:100%; border:none; background:none;"
| | This electronic textbook is a student-contributed open-source text covering a variety of topics on process optimization. |
| | style="text-align:center; white-space:nowrap; color:#000;" |
| | <br /> |
| <div style="font-size:162%; border:none; margin:0; padding:.1em; color:#000;">Welcome to the Cornell University Computational Optimization Open Textbook</div> | | 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]. |
| | <br /> |
| | ---- |
| | <br /><br /> |
| | <font size="6">Cornell University Open Text Book on Computational Optimization</font> |
|
| |
|
| This electronic textbook is a student-contributed open-source text covering a variety of topics on process optimization.<br />
| | {| class="wikitable" style="padding: 1em; text-align:left" |
| '''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].''' | | |- valign="top" |
| |} | | |width = "400pt"|<br />''' 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 />''' Mixed-Integer Linear Programming (MILP)''' |
| | # [[Facility location problems]] |
| | # [[Traveling salesman problems]] |
| | # [[Mixed-integer cuts]] |
| | # [[Disjunctive inequalities]] |
| | # [[Lagrangean duality]] |
| | # [[Column generation algorithms]] |
| | # [[Heuristic algorithms]] |
| | # [[Branch and cut]] |
| | <br /> |
| | |
| | |- valign="top" |
| | |<br />''' 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 />''' 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 />''' Global Optimization''' |
| | # [[Exponential transformation]] |
| | # [[Logarithmic transformation]] |
| | # [[McCormick envelopes]] |
| | # [[Piecewise linear approximation]] |
| | # [[Spatial branch and bound method]] |
| | <br /> |
| | |
| | |<br />''' Optimization under Uncertainty''' |
| | # [[Stochastic programming]] |
| | # [[Chance-constraint method]] |
| | # [[Fuzzy programming]] |
| | # [[Classical robust optimization]] |
| | # [[Adaptive robust optimization]] |
| | # [[Data driven robust optimization]] |
| | <br /> |
| | |
| | |
| | |- valign="top" |
| | |
| | |
| | |<br />''' Optimization for Machine Learning and Data Analytics''' |
| | # [[Stochastic gradient descent]] |
| | # [[Moment]] |
| | # [[RMSProp]] |
| | # [[ADAM]] |
| | <br /> |
| | |
| | |<br />''' Featured Applications''' |
| | # [[Wing Shape Optimization]] |
| | # [[Applying Optimization in Game Theory]] |
| | <br /> |
|
| |
|
| {| id="mp-upper" style="width: 100%; margin:6px 0 0 0; background:none; border-spacing: 0px;"
| |
| | class="MainPageBG" style="width:50%; border:1px solid #cef2e0; background:#f5fffa; vertical-align:top; color:#000;" |
| |
| {| id="mp-left" style="width:100%; vertical-align:top; background:#f5fffa;"
| |
| ! 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>
| |
| |-
| |
| | style="color:#000;" | <div id="mp-tfa" style="padding:2px 5px 5px 15px">
| |
| <li>[[Duality]]</li>
| |
| <li>[[Simplex algorithm]]</li>
| |
| <li>[[Computational complexity]]</li>
| |
| <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>
| |
|
| |
|
| |} | | |} |
|
| |
|
| | 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>
| |
| </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>
| |
| |}
| |
| |}
| |
|
| |
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