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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>
! 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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       <li>[[Duality]]</li>
       <li>[[Duality]]</li>
       <li>[[Simplex algorithm]]</li>
       <li>[[Simplex algorithm]]</li>
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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>
! 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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       <li>[[Line search methods]]</li>
       <li>[[Line search methods]]</li>
       <li>[[Trust-region methods]]</li>
       <li>[[Trust-region methods]]</li>
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       <li>[[Geometric programming]]</li>
       <li>[[Geometric programming]]</li>
       <li>[[Nondifferentiable Optimization]]</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>
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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>
! 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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       <li>[[Exponential transformation]]</li>
       <li>[[Exponential transformation]]</li>
       <li>[[Logarithmic transformation]]</li>
       <li>[[Logarithmic transformation]]</li>
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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>
! 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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       <li>[[Markov decision process]]</li>
       <li>[[Markov decision process]]</li>
       <li>[[Bellman equation]]</li>
       <li>[[Bellman equation]]</li>
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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>
! 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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       <li>[[Facility location problem]]</li>
       <li>[[Facility location problem]]</li>
       <li>[[Traveling salesman problem]]</li>
       <li>[[Traveling salesman problem]]</li>
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       <li>[[Unit commitment problem]]</li>
       <li>[[Unit commitment problem]]</li>
       <li>[[Portfolio optimization]]</li>
       <li>[[Portfolio optimization]]</li>
      <li>[[A-star algorithm]]</li>
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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;"> Emerging Applications</h2>
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      <li>[[Wing shape optimization]]</li>
      <li>[[Optimization in game theory]]</li>
      <li>[[Quantum computing for optimization]]</li>
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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>
! 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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       <li>[[Mixed-integer cuts]]</li>
       <li>[[Mixed-integer cuts]]</li>
       <li>[[Disjunctive inequalities]]</li>
       <li>[[Disjunctive inequalities]]</li>
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       <li>[[Heuristic algorithms]]</li>
       <li>[[Heuristic algorithms]]</li>
       <li>[[Branch and cut]]</li>
       <li>[[Branch and cut]]</li>
       <li>[[Local branching]]</li>
       <li>[[Local branching]]</li></div>
      <li>[[Feasibility pump]]</li>
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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>
! 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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       <li>[[Signomial problems]]</li>
       <li>[[Signomial problems]]</li>
       <li>[[Mixed-integer linear fractional programming (MILFP)]]</li>
       <li>[[Mixed-integer linear fractional programming (MILFP)]]</li>
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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>
! 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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       <li>[[Stochastic programming]]</li>
       <li>[[Stochastic programming]]</li>
       <li>[[Chance-constraint method]]</li>
       <li>[[Chance-constraint method]]</li>
       <li>[[Fuzzy programming]]</li>
       <li>[[Fuzzy programming]]</li>
       <li>[[Classical robust optimization]]</li>
       <li>[[Classical robust optimization]]</li>
      <li>[[Distributionally robust optimization]]</li>
       <li>[[Adaptive robust optimization]]</li>
       <li>[[Adaptive robust optimization]]</li>
       <li>[[Data driven robust optimization]]</li>
       <li>[[Data driven robust optimization]]</li>
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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>
! 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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       <li>[[Stochastic gradient descent]]</li>
       <li>[[Stochastic gradient descent]]</li>
       <li>[[Momentum]]</li>
       <li>[[Momentum]]</li>
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       <li>[[RMSProp]]</li>
       <li>[[RMSProp]]</li>
       <li>[[Adam]]</li>
       <li>[[Adam]]</li>
      <li>[[Alternating direction method of multiplier (ADMM)]]</li>
       <li>[[Frank-Wolfe]]</li>
       <li>[[Frank-Wolfe]]</li>
       <li>[[Sparse Reconstruction with Compressed Sensing]]</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>
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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;">Black-box Optimization</h2>
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      <li>[[Protein folding problem]]</li>
      <li>[[Wing shape optimization]]</li>
      <li>[[Optimization in game theory]]</li>
       <li>[[Bayesian optimization]]</li>
       <li>[[Bayesian optimization]]</li>
       <li>[[Quantum computing for optimization]]</li>
       <li>[[Genetic algorithm]]</li>
      <li>[[Simulated annealing]]</li>
      <li>[[Particle swarm optimization]]</li>
      <li>[[Differential evolution]]</li>
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Latest revision as of 17:35, 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