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|- valign="top"
|width = "400pt"|<br />'''&nbsp;&nbsp;Linear Programming (LP)'''
|width = "400pt"|<br />'''&nbsp;&nbsp;Linear Programming (LP)'''
# [[Duality]]
# [[Computational complexity]]  
# [[Computational complexity]]  
# [[Matrix game (LP for game theory)]]
# [[Network flow problem]]  
# [[Network flow problem]]  
# [[Interior-point method for LP]]  
# [[Interior-point method for LP]]  
# [[Optimization with absolute values]]
# [[Optimization with absolute values]]
# [[Matrix game (LP for game theory)]]
<br />
<br />


|width = "400pt"|<br />'''&nbsp;&nbsp;Mixed-Integer Linear Programming (MILP)'''
|width = "400pt"|<br />'''&nbsp;&nbsp;Mixed-Integer Linear Programming (MILP)'''
# [[Facility location problems]]
# [[Traveling salesman problems]]
# [[Mixed-integer cuts]]  
# [[Mixed-integer cuts]]  
# [[Disjunctive inequalities]]  
# [[Disjunctive inequalities]]  
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# [[Heuristic algorithms]]
# [[Heuristic algorithms]]
# [[Branch and cut]]
# [[Branch and cut]]
# [[Local branching]]
# [[Feasibility pump]]
<br />
<br />


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# [[Convex Generalized disjunctive programming (GDP)]]
# [[Convex Generalized disjunctive programming (GDP)]]
# [[Nonconvex Generalized disjunctive programming (GDP)]]
# [[Nonconvex Generalized disjunctive programming (GDP)]]
# [[Branch and bound (BB)]]
# [[Branch and bound (BB) for MINLP]]
# [[Branch and cut for MINLP]]
# [[Branch and cut for MINLP]]
# [[Generalized Benders decomposition (GBD)]]
# [[Generalized Benders decomposition (GBD)]]
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|- valign="top"
|- valign="top"


|<br />'''&nbsp;&nbsp;Global Optimization'''
|<br />'''&nbsp;&nbsp; Deterministic Global Optimization'''
# [[Exponential transformation]]
# [[Exponential transformation]]
# [[Logarithmic transformation]]
# [[Logarithmic transformation]]
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# [[Fuzzy programming]]
# [[Fuzzy programming]]
# [[Classical robust optimization]]
# [[Classical robust optimization]]
# [[Distributionally robust optimization]]
# [[Adaptive robust optimization]]
# [[Adaptive robust optimization]]
# [[Data driven robust optimization]]
# [[Data driven robust optimization]]
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|<br />'''&nbsp;&nbsp;Optimization for Machine Learning and Data Analytics'''
|<br />'''&nbsp;&nbsp;Optimization for Machine Learning and Data Analytics'''
# [[Stochastic gradient descent]]  
# [[Stochastic gradient descent]]  
# [[Moment]]
# [[Momentum]]
# [[AdaGrad]]
# [[RMSProp]]
# [[RMSProp]]
# [[ADAM]]
# [[Adam]]
# [[Alternating direction method of multiplier (ADMM)]]
# [[Frank-Wolfe]]
<br />
<br />


|<br />'''&nbsp;&nbsp;Featured Applications'''
|<br />'''&nbsp;&nbsp;Featured Applications'''
# [[Facility location problems]]
# [[Traveling salesman problems]]
# [[Wing Shape Optimization]]
# [[Wing Shape Optimization]]
# [[Applying Optimization in Game Theory]]
# [[Applying Optimization in Game Theory]]

Revision as of 19:40, 26 August 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.



Cornell University Open Text Book on Computational Optimization


  Linear Programming (LP)
  1. Duality
  2. Computational complexity
  3. Network flow problem
  4. Interior-point method for LP
  5. Optimization with absolute values
  6. Matrix game (LP for game theory)
  Mixed-Integer Linear Programming (MILP)
  1. Mixed-integer cuts
  2. Disjunctive inequalities
  3. Lagrangean duality
  4. Column generation algorithms
  5. Heuristic algorithms
  6. Branch and cut
  7. Local branching
  8. Feasibility pump



  NonLinear Programming (NLP)
  1. Line search methods
  2. Trust-region methods
  3. Interior-point method for NLP
  4. Conjugate gradient methods
  5. Quasi-Newton methods
  6. Quadratic programming
  7. Sequential quadratic programming
  8. Subgradient optimization
  9. Mathematical programming with equilibrium constraints
  10. Dynamic optimization
  11. Geometric programming
  12. Nondifferentiable Optimization
  Mixed-Integer NonLinear Programming (MINLP)
  1. Signomial problems
  2. Mixed-integer linear fractional programming (MILFP)
  3. Convex Generalized disjunctive programming (GDP)
  4. Nonconvex Generalized disjunctive programming (GDP)
  5. Branch and bound (BB) for MINLP
  6. Branch and cut for MINLP
  7. Generalized Benders decomposition (GBD)
  8. Outer-approximation (OA)
  9. Extended cutting plane (ECP)



   Deterministic Global Optimization
  1. Exponential transformation
  2. Logarithmic transformation
  3. McCormick envelopes
  4. Piecewise linear approximation
  5. Spatial branch and bound method
  Optimization under Uncertainty
  1. Stochastic programming
  2. Chance-constraint method
  3. Fuzzy programming
  4. Classical robust optimization
  5. Distributionally robust optimization
  6. Adaptive robust optimization
  7. Data driven robust optimization




  Optimization for Machine Learning and Data Analytics
  1. Stochastic gradient descent
  2. Momentum
  3. AdaGrad
  4. RMSProp
  5. Adam
  6. Alternating direction method of multiplier (ADMM)
  7. Frank-Wolfe
  Featured Applications
  1. Facility location problems
  2. Traveling salesman problems
  3. Wing Shape Optimization
  4. Applying Optimization in Game Theory




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