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**Optimization Methods**

In optimization of a project, the plan objective could be only to diminish the cost of manufacture or to exploit the competence of manufacture. An optimization procedure is a process which is performed iteratively by associating various answers till an finest or a reasonable explanation is found. With the advent of processors, optimization has converted a part of computer aided enterprise events. There are two discrete types of optimization procedures commonly used today.

**(a) Deterministic Algorithms.**

They use precise rules for affecting one explanation to other. These algorithms are in use to suite around times and have remained efficaciously applied for many design difficulties.

**(b) Stochastic Algorithms.**

The stochastic algorithms are in countryside with probabilistic conversion rules. These are achievement admiration due to convinced properties which deterministic procedures do not consume.

**Steps to follow in optimization formulation.**

First decide need of optimization next choose design variables then formula constraints next formulate objective function then set-up variable bounds and choose an suitable algorithm with this step we can obtain the solution.

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Optimization is the process to optimize the things in order to improve them. There is need of optimization because of the requirement of an efficient and decision making approach during the designing of a system. Optimization methods refer to the methods that can be used for the process of optimization.The optimization methods require many elements. These elements include objective function, predictive model and variables. Objective function is required to provide a scalar quantitative performance measure that must be maximized or minimized. The predictive model is required for describing the system behavior. Variables which appear in the predictive model have to be adjusted in such a way that they satisfy the constraints that are the limits of the system performance.

Optimization models include Single x Multiobjective models, Static x Dynamic models and Deterministic x Stochastic models. There are two types of optimization methods that are constrained optimization and unconstrained optimization. Constrained optimization methods are used for the problems that have constraints and the unconstrained optimization can be used for the problems that do not have any constraints. The technique that can be used for the constrained optimization is lagrangian multipliers to find the optimal value of the function which is Optimization Methodsed to equality constraints.

The applications of optimization methods in statistics are flux lines with hard core interactions, vortex glass with strong screening, random field ising systems, spin glasses, statistical physics of complexity, random bond potts model, periodic media wetting phenomenon in random systems, Robust optimization, Network flows, Lagrangean methods, Heuristics and approximation algorithms, Conjugate gradient methods, Affine scaling algorithm, Branch and bound and cutting planes, Stochastic programming, Combinatorial optimization, Constraint satisfaction, Convex Relaxations, Branch-and-Bound Method, Quasi-Newton, Subgradient Methods

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**Few Topics are:**

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Linear programming

Systems of linear equations

Graph theory

Matrix Multiplication

Matrices

Convex Optimization

Network flow

Computationally optimisation

Genetic algorithms

Integer programming