The objective of this course is to introduce optimization techniques to engineering students, with an emphasis on problems arising in Chemical Engineering applications. The course includes both linear and nonlinear programming problems.The first portion of the course introduces the basic concepts in optimization and how to obtain a mathematical representation of the optimization problem. The second portion of the course describesdifferent solution techniques that can be used to actually solve such problems. Finally, a set of software tools for solution of optimization problems are also discussed.Upon successful completion of this course, the student will be able to understand the basic theoretical principles in optimization, formulate the optimization problem, and choose appropriate method/solver for solution of the optimization problem.
INTENDED AUDIENCE : Chemical Engineering, Biochemical Engineering, Agriculture Engineering
PREREQUISITES : Nil
INDUSTRY SUPPORT : This course may be of general interest to many chemical process industries such as:
(1) Indian Oil Corporation Ltd.
(2) Hindustan Petroleum Corporation Ltd.
(3) Haldia Petrochemicals Ltd
Week 1: Introduction to Optimization(Statement of optimization problems, Classification of optimization problems,
Examples from engineering applications, Review of linear algebra)
Week 2: Optimization Problem Formulation (Models for optimization, Optimization problems in chemical/biochemical
Week 3: Basic Concepts of Optimization – I (Continuity of functions, Unimodal and multimodal functions, Optimality
criteria for unconstrained single variable functions)
Week 4: Basic Concepts of Optimization – II (Optimality criteria for unconstrained multivariable functions, Equality
constrained problems, Lagrange multipliers, Kuhn Tucker conditions)
Week 5: Unconstrained Single Variable Optimization: Methods and Applications (Region elimination methods, Methods
requiring derivatives: Newton-Raphson method, Bisection method, Secant method)
Week 6: Unconstrained Multivariable Optimization: Direct Search Methods (Simplex method, Hooke-Jeeves pattern search
method, Powell’s conjugate direction method)
Week 7: Unconstrained Multivariable Optimization: Gradient Based Methods (Cauchy’s method, Newton’s method, Marquardt method)
Week 8: Introduction to Linear Programming (Formulation of linear programming models, Graphical solution, Linear programs in standard form)
Week 9: Linear Programming: The Simplex Method (Simplex method, Use of artificial variables, Two phase method)
Week 10: Constrained Nonlinear Programming (Penalty function method, Lagrange multiplier method)
Week 11: Applications of Optimization (Optimization of various chemical and biochemical processes)
Week 12: Software Tools for Optimization