What Is Optimization Toolbox?

1 Getting StartedOptimization ExampleThis section presents an example that illustrates how to solve an optimizationproblem using the toolbox function lsqlin, which solves linear least squaresproblems. This section covers the following topics:• “The Problem” on page 1-4• “Setting Up the Problem” on page 1-4• “Finding the Solution” on page 1-5• “More Examples” on page 1-6The ProblemThe problem in this example is to find the point on the planethat is closest to the origin. The easiest way to solve this problem is tominimize the square of the distance from a pointon the planeto the origin, which returns the same optimal point as minimizing the actualdistance. Since the square of the distance from an arbitrary pointto the origin is, you can describe the problem as follows:subject to the constraintThe function f(x) iscalledtheobjective function andis anequality constraint. More complicated problems might contain other equalityconstraints, inequality constraints, and upper or lower bound constraints.Setting Up the ProblemThis section shows how to set up the problem before applying the functionlsqlin, which solves linear least squares problems of the following form:1-4