10.90.136.11: Created page with "= Nonlinear Optimization = * '''Course name:''' Nonlinear Optimization * '''Course number:''' == Course Characteristics == === Key concepts of the..."

2021-07-30T10:48:04Z

Created page with "= Nonlinear Optimization = * '''Course name:''' Nonlinear Optimization * '''Course number:''' == Course Characteristics == === Key concepts of the..."

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= Nonlinear Optimization =

* '''Course name:''' Nonlinear Optimization
* '''Course number:'''

== Course Characteristics ==

=== Key concepts of the class ===

* Methods of nonlinear optimization
* Solution of optimization problems

=== What is the purpose of this course? ===

The main purpose of this course...

* The formation of professional competencies in accordance with the Federal State Educational Standard
* Fundamentalization of education
* Training of a specialist with knowledge and skills related to optimization problems in mechatronics and robotics based on meaningful formulation and subsequent formalization, and solution.

=== Course objectives based on Bloom’s taxonomy ===

=== - What should a student remember at the end of the course? ===

By the end of the course, the students should be able to remember and recognize:

* The role and place of optimization methods in the development of modern mechatronics and robotics,
* Terminology of optimization problems,
* Classification of optimization tasks,
* Models and methods of optimization theory, tasks effectively solved with their use,
* Concepts and principles of theories related to solving mathematical programming problems,
* Optimization software

=== - What should a student be able to understand at the end of the course? ===

By the end of the course, the students should be able to describe and explain

* Formalized description of optimization problems for constructing mathematical models,
* Optimization methods and theory for solving problems of mechatronic and robotic systems (meaningful statement, choice of solution method, implementation),
* Results of solving problems of mathematical optimization,
* Instrumental (software) tools for analytical and numerical solution of optimization problems

=== - What should a student be able to apply at the end of the course? ===

By the end of the course, the students should be able to ...

* Skills to formalize optimization tasks,
* Information handling technologies for solving finite-dimensional optimization problems,
* Skills in using numerical methods to find the optimal solution for successful problem solving,
* The main types of information systems and general-purpose applications for solving practical optimization problems with their help,
* Algorithms for solving problems of mathematical optimization

=== Course evaluation ===

{|
|+ Course grade breakdown
!
!
!align="center"| '''Proposed points'''
|-
| Labs/seminar classes
| 20
|align="center"|
|-
| Interim performance assessment
| 30
|align="center"|
|-
| Exams
| 50
|align="center"|
|}

The course grades are given according to the following rules: Homework assignments (4) = 20 pts, Quizzes (4) = 40 pts, Term project = 40 pts

=== Grades range ===

{|
|+ Course grading range
!
!
!align="center"| '''Proposed range'''
|-
| A. Excellent
| 90-100
|align="center"|
|-
| B. Good
| 75-89
|align="center"|
|-
| C. Satisfactory
| 60-74
|align="center"|
|-
| D. Poor
| 0-59
|align="center"|
|}

If necessary, please indicate freely your course’s grading features.

=== Resources and reference material ===

* Dimitri Bertsekas. Nonlinear Programming: 3rd Edition. Athena Scientific, 2016. ISBN: 1886529051
* Nocedal J., Wright S. Numerical optimization. Springer Science and Business Media, 2006
* Dimitri Bertsekas. Nonlinear Programming: 2nd Edition. Belmont, MA: Athena Scientific Press, 1999. ISBN: 1886529000.

== Course Sections ==

The main sections of the course and approximate hour distribution between them is as follows:

{|
|+ Course Sections
!align="center"| '''Section'''
! '''Section Title'''
!align="center"| '''Teaching Hours'''
|-
|align="center"| 1
| Dynamics and electrodynamics
|align="center"| 6
|-
|align="center"| 2
| Electric motors
|align="center"| 6
|-
|align="center"| 3
| Transmission mechanisms and sensors
|align="center"| 4
|-
|align="center"| 4
| Control systems
|align="center"| 6
|}

=== Section 1 ===

==== Section title: ====

Unconstrained Optimization

=== Topics covered in this section: ===

* Optimality Conditions
* Gradient Methods
* Convergence Analysis of Gradient Methods
* Rate of Convergence
* Newton and Gauss-Newton Methods
* Additional Methods

=== What forms of evaluation were used to test students’ performance in this section? ===

<div class="tabular">

|a|c| & '''Yes/No''' 
Development of individual parts of software product code & 0 
Homework and group projects & 1 
Midterm evaluation & 0 
Testing (written or computer based) & 1 
Reports & 0 
Essays & 0 
Oral polls & 0 
Discussions & 1 

</div>
=== Typical questions for ongoing performance evaluation within this section ===

# What are the optimal conditions?
# Describe the idea of gradient methods.
# What is the rate of convergence?
# Explain Newton’s optimization method.
# What are the least squares problems?

=== Typical questions for seminar classes (labs) within this section ===

# Implement Newton’s method (e.g., using Matlab).
# Implement the gradient method.
# Implement Gauss-Newton method.
# Implement the nonderivative method.
# Implement the conjugate direction method.

=== Test questions for final assessment in this section ===

# What is Newton’s optimization method?
# What are the gradient methods?
# Explain Quasi-Newton optimization method.

=== Section 2 ===

==== Section title: ====

Optimization Over a Convex Set

=== Topics covered in this section: ===

* Optimality Conditions
* Feasible Direction Methods
* Alternatives to Gradient Projection
* Two-Metric Projection Methods
* Manifold Suboptimization Methods

=== What forms of evaluation were used to test students’ performance in this section? ===

<div class="tabular">

|a|c| & '''Yes/No''' 
Development of individual parts of software product code & 0 
Homework and group projects & 1 
Midterm evaluation & 0 
Testing (written or computer based) & 1 
Reports & 0 
Essays & 0 
Oral polls & 0 
Discussions & 1 

</div>
=== Typical questions for ongoing performance evaluation within this section ===

# What are the optimal conditions?
# Descent directions and stepsize rules.
# Feasible directions and stepsize rules based on projection.
# Convergence analysis.
# What is convex set?

=== Typical questions for seminar classes (labs) within this section ===

# Implement the conditional gradient method.
# Implement gradient projection method.
# Implement two-metric projection method.
# Implement manifold suboptimization Method.

=== Test questions for final assessment in this section ===

# Explain optimality conditions
# Explain feasible direction methods
# What are alternatives to gradient projection?
# Explain twomMetric projection methods.
# Describe manifold suboptimization methods.

=== Section 3 ===

==== Section title: ====

Constrained Optimization and Lagrange Multipliers

==== Topics covered in this section: ====

* Necessary conditions for equality constraints
* Sufficient conditions and sensitivity analysis
* Inequality constraints
* Linear constraints and duality
* Barrier and interior point methods
* Penalty and augmented Lagrangian methods
* Lagrangian and Primal-Dual Interior Point Methods

=== What forms of evaluation were used to test students’ performance in this section? ===

<div class="tabular">

|a|c| & '''Yes/No''' 
Development of individual parts of software product code & 0 
Homework and group projects & 0 
Midterm evaluation & 0 
Testing (written or computer based) & 1 
Reports & 0 
Essays & 0 
Oral polls & 1 
Discussions & 1 

</div>
=== Typical questions for ongoing performance evaluation within this section ===

# The penalty approach
# The elimination approach
# The Lagrangian function
# The augmented Lagrangian approach
# Karush-Kuhn-Tucker optimally conditions
# Sufficiency conditions and Lagrangian minimization

==== Typical questions for seminar classes (labs) within this section ====

# Implement barrier and interior point methods
# Implement the quadratic penalty function method
# Implement multiplier method
# Implement Newton-like method for equality constraints
# Implement primal-dual point method

==== Test questions for final assessment in this section ====

# Describe sufficiency conditions and Lagrangian minimization
# What are Karush-Kuhn-Tucker optimally conditions?
# Explain penalty and augmented Lagrangian methods
# Describe barrier and interior point methods

=== Section 3 ===

==== Section title: ====

Duality, convex programming and dual methods

==== Topics covered in this section: ====

* The dual problem
* Convex cost - linear constraints
* Convex cost - convex constraints
* Conjugate functions and Fenchel duality
* Dual ascent methods for differentiable dual problems
* Nondifferentiable optimization methods

=== What forms of evaluation were used to test students’ performance in this section? ===

<div class="tabular">

|a|c| & '''Yes/No''' 
Development of individual parts of software product code & 0 
Homework and group projects & 1 
Midterm evaluation & 0 
Testing (written or computer based) & 1 
Reports & 0 
Essays & 0 
Oral polls & 1 
Discussions & 1 

</div>
=== Typical questions for ongoing performance evaluation within this section ===

# Lagrange multipliers
# Characterization of primal and dual optimal solutions
# Network optimization
# Coordinate ascent for quadratic programming.
# Subgradient methods

==== Typical questions for seminar classes (labs) within this section ====

# Implement subgradient method
# Implement approximate and incremental subgradient methods
# Implement cutting plane method.
# Implement ascent and approximate ascent methods.

==== Test questions for final assessment in this section ====

# The weak duality theorem.
# Separable problems and their geometry
# Lagrangian relaxation

BSc:NonlinearOptimization - Revision history

10.90.136.11: Created page with "= Nonlinear Optimization = * '''Course name:''' Nonlinear Optimization * '''Course number:''' == Course Characteristics == === Key concepts of the..."