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MTH403 Short Notes for Final Term and Mid Term. If you are a student of MTH403 – Optimization Techniques, you know how important it is to have a good set of notes that can help you prepare for both the mid-term and final exams. In this article, we will provide you with a comprehensive set of short notes that will help you revise the entire syllabus of MTH403.

## Introduction to MTH403

MTH403 is an introductory course to optimization techniques that are widely used in the field of engineering, economics, and computer science. The course covers different optimization techniques like linear programming, non-linear programming, integer programming, and dynamic programming.

## Linear Programming

Linear programming is a technique used to optimize a linear objective function, subject to linear constraints. The objective function is a linear combination of the decision variables, and the constraints are linear inequalities or equalities.

### Simplex Method

The simplex method is an iterative algorithm that is used to solve linear programming problems. It starts with an initial feasible solution and moves towards the optimal solution by improving the objective function in each iteration.

### Duality

The duality principle is a fundamental concept in linear programming that relates the primal problem to its dual problem. The dual problem is a mathematical formulation of the same problem, where the objective function and the constraints are swapped.

## Non-Linear Programming

Non-linear programming is a technique used to optimize a non-linear objective function, subject to non-linear constraints. The objective function is a non-linear function of the decision variables, and the constraints are non-linear inequalities or equalities.

### Gradient Descent

Gradient descent is an optimization algorithm that is used to find the local minimum of a function. It starts with an initial guess and iteratively moves towards the minimum by taking small steps in the direction of the negative gradient of the function.

### Newton’s Method

Newton’s method is another optimization algorithm that is used to find the local minimum of a function. It starts with an initial guess and iteratively moves towards the minimum by using the second derivative of the function.

## Integer Programming

Integer programming is a technique used to optimize an objective function, subject to integer constraints. The decision variables are required to take integer values, which makes the problem more complex than linear programming.

### Branch and Bound

Branch and bound is an algorithm used to solve integer programming problems. It starts with a relaxation of the problem, where the integer constraints are removed. It then uses a tree-based search to find the optimal solution of the integer problem.

## Dynamic Programming

Dynamic programming is a technique used to solve optimization problems that have a recursive structure. The solution to the problem is found by breaking it down into smaller sub problems and solving them recursively.

### Bellman’s Principle of Optimality

Bellman’s principle of optimality is a fundamental concept in dynamic programming. It states that an optimal policy has the property that, whatever the initial state and the initial decision are, the remaining decisions must constitute an optimal policy with regard to the state resulting from the first decision.

## Conclusion

In conclusion, MTH403 is a crucial course that covers different optimization techniques used in various fields of study. These short notes provide a concise and comprehensive overview of the entire syllabus of MTH403, which can help you prepare for both the mid-term and final exams.

## FAQs

- What is MTH403?

- MTH403 is an introductory course to optimization techniques.

- What are the different optimization techniques covered in MTH403?

- Linear programming, non-linear programming, integer programming, and dynamic programming.

- What is the simplex method?

- The simplex method is an iterative algorithm used to solve linear programming problems.

- What is gradient descent?

- Gradient descent is an optimization algorithm used to find the local minimum of a function.

- What is the duality principle?

- The duality principle is a fundamental concept in linear programming that relates the primal problem to its dual problem.

### MTH403 Short Notes for Final Term and Mid Term

- MTH403 Handwritten Short Notes PDF –
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