What Is Optimization Toolbox?

2 TutorialLarge-Scale Examples• “Introduction” on page 2-40• “Problems Covered by Large-Scale Methods” on page 2-41• “Nonlinear Equations with Jacobian” on page 2-45• “Nonlinear Equations with Jacobian Sparsity Pattern” on page 2-47• “Nonlinear Least-Squares with Full Jacobian Sparsity Pattern” on page2-50• “Nonlinear Minimization with Gradient and Hessian” on page 2-51• “Nonlinear Minimization with Gradient and Hessian Sparsity Pattern”on page 2-53• “Nonlinear Minimization with Bound Constraints and BandedPreconditioner” on page 2-55• “Nonlinear Minimization with Equality Constraints” on page 2-59• “Nonlinear Minimization with a Dense but Structured Hessian andEquality Constraints” on page 2-61• “Quadratic Minimization with Bound Constraints” on page 2-65• “Quadratic Minimization with a Dense but Structured Hessian” on page2-67• “Linear Least-Squares with Bound Constraints” on page 2-72• “Linear Programming with Equalities and Inequalities” on page 2-73• “Linear Programming with Dense Columns in the Equalities” on page 2-75IntroductionSome of the optimization functions include algorithms for continuousoptimization problems especially targeted to large problems with sparsity orstructure. The main large-scale algorithms are iterative, i.e., a sequenceof approximate solutions is generated. In each iteration a linear system is(approximately) solved. The linear systems are solved using the sparse matrixcapabilities of MATLAB and a variety of sparse linear solution techniques,both iterative and direct.2-40