Course program
1) Introduction to the course with an examination of problems of interest to the process industry and related formulation of constrained and unconstrained optimization problems for optimal parameter estimation
* example of an optimal scheduling problem
* production optimization of a refinery and related formulation and solution of linear programming problems
* optimal thickness of the insulation of a pipeline.
* optimization of the surface area of a heat exchanger train.
* nonlinear regression of liquid-vapor equilibrium data.
2) Unconstrained optimization
Formulation of the linear and nonlinear least squares problem
Characterization of quadratic functions : role of eigenvalues/eigenvectors of the Hessiana matrix
Convexity of a function
Directions of descent and directional derivatives
Necessary and/or sufficient first- and second-order conditions for a point of minimum
Antigradient method (steepest descent)
Newton's method
Finite difference representation of the first and second derivatives of the objective function
Conjugate direction method for quadratic functions
Conjugate gradient method for nonquadratic functions
Method of random directions
Powell's method
Outline of the simpllex method
Exact unidirectional search methods (Newton unidirectional and bisection method)
Speed convergence analysis : linear, superlinear and quadratic convergence
2) Constrained optimization
Definition of useful and admissible directions for inequality constraints and equality constraints
Definition of a convex problem
Necessary and/or sufficient first and second order conditions for a point of minimum (Lagrangian function method and KKT conditions)
Reduced gradient method
Rosen's method
Zoutendijk's method
Penalty function method (internal method and external method)
3) Introduction to multivariate analysis.
Mean value, variance, skewness factor
Correlation analysis between data sets
Variance/covariance and correlation matrices
Principal component analysis (PCA)
Definition of confidence ellipses, outliers and biplots.
4) Introduction to Matlab
Implementation of code for linear least squares
Implementation of the code for Newton's method
Implementation of the code for the random directions method
Prerequisites
Calculus I and II
Books
Handouts prepared by the lecturer on all topics covered
Optimisation of chemical processes, Himmelblau
Frequency
Participation in the course is not mandatory, but strongly recommended.
Exam mode
In the written exam, 2/3 exercises are assigned to be completed in a time frame of 2 1/2 hours using only the scientific calculator.
Following the correction of the assignment, all students view the result and are invited to discuss any errors made with the teacher.
In A.Y. 2023/2024, two in-progress tests (waivers) were conducted one in the middle and one at the end of the course (last day of class)
Lesson mode
The professor conducts the course entirely on blackboard, conducting several exercises some of which are aimed at using Matlab to solve problems of interest
