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B018804 - NUMERICAL OPTIMIZATION
Main information
Teaching Language
Course Content
Suggested readings
Learning Objectives
Prerequisites
Teaching Methods
Type of Assessment
Course program
Academic Year 2016-17
Coorte 2016 - Second Cycle Degree in MATHEMATICS
Course year
First year -
Belonging Department
Mathematics and Computer Science "Ulisse Dini" (DIMAI)
Course Type
Single education field course
Scientific Area
MAT/08 - NUMERICAL ANALYSIS
Credits
9
Teaching Hours
72
Teaching Term
⇒
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
Mutuality
Course teached as:
B018804 - OTTIMIZZAZIONE NUMERICA
Second Cycle Degree in MATHEMATICS
Curriculum GENERALE
B018804 - OTTIMIZZAZIONE NUMERICA
Second Cycle Degree in MATHEMATICS
Curriculum GENERALE
Teaching Language
Italian
Course Content
Main characteristics of numerical methods for unconstrained nonlinear programming. Optimality conditions for constrained optimization. Methods for Linear and Quadratic Programming problems. Basic Fortran instructions. Public domain software.
Suggested readings (Search our library's catalogue)
J. Nocedal, S.J. Wright, "Numerical Optimization", 2nd ed., 2006
Learning Objectives
Knowledge of optimality theory for linear programming and constrained nonlinear programming.
Knowledge of the main numerical optimization methods for linear and constrained nonlinear programming and of their theoretical background.
Knowledge of the main numerical optimization methods for linear and constrained nonlinear programming and of their theoretical background.
Prerequisites
Courses recommended: first level courses of Mathematical Analysis and Numerical Analysis
Teaching Methods
Frontal lessons and experience in laboratory
Type of Assessment
Oral test about lecture’s topics and laboratory activities.
Course program
Unconstrained nonlinear programming: optimality conditions. Gradient method and Conjugate Gradient method for objective quadratic functions. Gradient method, Newton method and quasi-Newton methods for nonlinear objective functions. Line-search globalization techniques. Use of public domain software.
Linear Programming: models formulation with examples from optimal resource allocation,
transportation problems.
Introduction to Linear programming: Basic Feasible points, feasible polytope, Optimality and Duality Theory, simplex method.
Primal Dual Interior Point methods: Introduction, central path, path-following methods: convergence theory . Public domain software for linear programming .
Constrained Nonlinear Optimization: models formulation with examples,
feasible directions, derivation of first order and second order conditions
Quadratic Programming: active set method. Extension of Interior Point methods to Quadratic Programming
Introduction to Fortran language: basic instructions, subroutines, libraries.
Linear Programming: models formulation with examples from optimal resource allocation,
transportation problems.
Introduction to Linear programming: Basic Feasible points, feasible polytope, Optimality and Duality Theory, simplex method.
Primal Dual Interior Point methods: Introduction, central path, path-following methods: convergence theory . Public domain software for linear programming .
Constrained Nonlinear Optimization: models formulation with examples,
feasible directions, derivation of first order and second order conditions
Quadratic Programming: active set method. Extension of Interior Point methods to Quadratic Programming
Introduction to Fortran language: basic instructions, subroutines, libraries.