Process Control and Optimization

7.

Process Optimization

7.1.

Introduction to Optimization

7.1.1.

Defining the Objective Function

7.1.2.

Types of Constraints

7.1.2.1.

Equality Constraints

7.1.2.2.

Inequality Constraints

7.1.3.

Decision Variables

7.1.4.

Feasible Region

7.2.

Basic Concepts in Optimization

7.2.1.

7.2.2.

7.2.3.

Local vs. Global Optima

7.2.4.

Necessary and Sufficient Conditions for Optimality

7.2.5.

Gradient and Hessian

7.3.

Unconstrained Optimization

7.3.1.

Single-Variable Optimization

7.3.1.1.

Analytical Methods

7.3.1.2.

Golden Section Search

7.3.1.3.

Fibonacci Search

7.3.1.4.

Newton-Raphson Method

7.3.2.

Multivariable Optimization

7.3.2.1.

Gradient-Based Methods

7.3.2.1.1.

Steepest Descent

7.3.2.1.2.

Conjugate Gradient

7.3.2.2.

Newton's Method

7.3.2.3.

Quasi-Newton Methods

7.3.2.3.1.

7.3.2.3.2.

7.4.

Constrained Optimization

7.4.1.

Linear Programming (LP)

7.4.1.1.

Problem Formulation

7.4.1.2.

Graphical Solution Method

7.4.1.3.

7.4.1.4.

7.4.1.5.

Sensitivity Analysis

7.4.2.

Nonlinear Programming (NLP)

7.4.2.1.

Problem Formulation

7.4.2.2.

Successive Quadratic Programming (SQP)

7.4.2.3.

Interior-Point Methods

7.4.2.4.

Lagrange Multipliers

7.4.2.5.

Karush-Kuhn-Tucker (KKT) Conditions

7.4.3.

Mixed-Integer Programming

7.4.3.1.

7.4.3.2.

Solution Methods

7.5.

Stochastic Optimization

7.5.1.

Genetic Algorithms

7.5.2.

Simulated Annealing

7.5.3.

Particle Swarm Optimization

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