Optimization-Programming-

Optimization Programming / Algorithm for finding minimum

Optimization

• Steepest descent search algorithm with and without Armijo Rule
• Newton's method
• Steepest Descent Algorithm Hessian matrix | inexact backtracking line search

Newton's Method (Armijo Rule)

Steepest Descent Search Algorithm (Backtracking)

Unconstrained non-linear optimization using MATLAB function, 'fminunc' to minimize Rosenbrock function

Nature and bio-inspired Moth-Flame Optimization In the last three decades, a great number of derive-free methods and algorithms have been developed for solving hard optimization problems; thse include the widely used, nature and bio-inspired, population based methaheuristics which are related to evolutionary computation and artificial intelligence

Matlab function, 'fmincon' for constrained optimization with initial values provided

Penalty Method to solve constrained minimization problem. Constraints are sued to define a penalty term which is added to the original objective function. Any point that is outside the feasible region will be penalized, penalty methods always favous those points which are in the feasible regin Additional Methods were compared: Genetic Algorithm Particle Swarm Optimization, PSO Simulated Annealing

Constrained Minimization using MATLAB toolboxes. MATLAB functions, 'fmincon', 'ga' and 'particleswarm' were used to solve the problem