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JNTUA College of Engineering (Autonomous), Ananthapuramu
Department of Computer Science & Engineering
Professional Elective-I
OPTIMIZATION TECHNIQUES

Corse Code: Semester V (R20) L T P C : 3 0 0 3
Course Objectives:
• The basic concepts of Optimization
• The emphasis of this course is on different classical Optimization techniques
linearprogramming and simplex algorithms.
• About optimality of balanced transportation Problems
• About Constrained and unconstrained nonlinear programming.
• About principle of optimality and dynamic programming

Course Outcomes (CO):
● To know how to formulate statement of optimization problem with or without constraints
● To know about classification of single and multivariable optimization problems
● To know about necessary and sufficient conditions in defining the optimization problems
● To understand how to formulate Kuhn-Tucker conditions and to solve numerical problems
UNIT-I: Introduction and Classical Optimization Techniques:
Statement of an Optimization problem – design vector – design constraints – constraint surface –
objective function – objective function surfaces – classification of Optimization problems. Classical
Optimization Techniques: Single variable Optimization – multi variable Optimization without
constraints – necessary and sufficient conditions for minimum /maximum – multivariable
Optimization with equality constraints. Solution by method of Lagrange multipliers – multivariable
Optimization with inequality constraints – Kuhn – Tucker conditions – Numerical examples.

UNIT-II:Linear Programming
Standard form of a linear programming problem – geometry of linear programming problems –
definitions and theorems – solution of a system of linear simultaneous equations – pivotal
reduction of a general system of equations – motivation to the simplex method – simplex
algorithm – Numerical examples.

UNIT-III:Nonlinear Programming – One Dimensional Minimization methods
Introduction, Unimodal function, Elimination methods- Unrestricted Search, Exhaustive Search,
Dichotomous Search, Fibonacci Method, Golden Section Method and their comparison; Interpolation
methods - Quadratic Interpolation Method, Cubic Interpolation Method and Direct Root Methods –
Numerical examples.

UNIT-IV:Unconstrained & Constrained Nonlinear Programming
Unconstrained Optimization Techniques: Introduction- Classification of Unconstrained
Minimization Methods, General Approach, Rate of Convergence, Scaling of Design Variables;
Direct Search methods- Random Search Methods, Grid Search Method, Pattern Directions,
Powell’s Method and Simplex Method

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