Optimization Using Pattern Search Method: MATLAB Programming

Define the objective function, or fitness function, to optimize with X1 and X2, and learn local versus global solutions in MATLAB.

Learn to write a MATLAB objective function that accepts a two-element vector and returns a scalar, saved on the MATLAB path, and tested with X1=2 and X2=3.

Vectorize the objective function to compute multiple input sets at once, speeding up MATLAB optimization. Save the vectorized function on the MATLAB path and verify outputs as a column vector.

Master passing extra parameters to MATLAB objective functions in pattern search, using four arguments: independent variable and a, b, c. Create and verify scripts with sample values a=4, b=2.1, c=4.

Pattern search finds a local minimum by polling around the current point with plus/minus directions, doubling the mesh on success and halving on failure, with no gradients needed.

Learn how pattern search, a direct search method, solves optimization problems without gradient information, including non-differentiable or non-continuous objectives. Explore using MATLAB's pattern search tool through practical examples.

Explore unconstrained pattern search minimization of a two-variable function, starting from [0,0], using MATLAB's pattern search to locate a local minimum.

Learn to solve optimization problems with linear inequality constraints using MATLAB's patternsearch, starting from x = [0.5; -0.5], and use A and b to locate the local minimum.

Apply pattern search in MATLAB to minimize a three-variable objective under a linear equality constraint by configuring Aeq and beq, using a zero starting point to locate the local minimum.

Explore pattern search with bound constraints in matlab to minimize the objective function, starting from x1=1 and x2=-5 under lb=[0, -inf] and ub=[inf, -3], using the pattern search function.

Minimize the objective and locate the minimum starting from x1 = -2, x2 = -2 while satisfying the nonlinear constraint with the pattern search in MATLAB.

Obtain the objective function value at the local minimum using the patternsearch function in MATLAB, returning x as the minimum location and fval as the minimum value, including constrained problems.

Learn how to find the global minimum with MATLAB's patternsearch by enabling the complete poll option through optimoptions, comparing local and global minima of an objective function.

Vectorize the objective and nonlinear constraint functions to accelerate the direct search method in MATLAB; enable complete poll and use vectorization to solve the optimization with two nonlinear constraints.

Learn to solve an optimization with six independent variables and linear constraints in MATLAB using pattern search method, optimoptions to enable parallel mode and complete poll, reaching the global minimum.

Use the global optimization toolbox by negating f(x) to g(x) and minimizing g(x) under nonlinear and bound constraints, demonstrated with MATLAB code and step-by-step files.

Explore stopping criteria in MATLAB's pattern search, including mesh tolerance, max iterations and function evaluations, with tips to adjust defaults using the options structure.

Learn how to obtain the exitflag and output from the pattern search function in MATLAB, including interpreting x, fval, iterations, and mesh size at convergence.