MATLAB Software

Michael L. Overton

Control

• HIFOO: H-infinity Fixed-Order Optimization
  (including low-order controller design for stabilization of multiple plants)

Optimization

• GRANSO: GRadient-based Algorithm for Non-Smooth Optimization
  (for nonsmooth, nonconvex optimization subject to nonsmooth, nonconvex constraints, based on a BFGS-SQP method. This code, written by former Ph.D. student Tim Mitchell, extends and improves upon HANSO.)
  
  
• HANSO: Hybrid Algorithm for Non-Smooth Optimization
  (for general unconstrained minimization: convex or nonconvex, smooth or nonsmooth, including BFGS and limited memory BFGS using a weak Wolfe line search and the gradient sampling method, which, unlike BFGS, has a nice convergence theory for nonsmooth optimization)
  
  
• NLCG: Nonlinear Conjugate Gradient
  (for smooth unconstrained minimization, with multiple variants of nonlinear CG, most notably Polak-Ribere constrained by Fletcher-Reeves, based on strong Wolfe line search)
  
  
• AFFPOLYMIN: Root Optimization for a Polynomial Family with an Affine Constraint
  (global minimization of the root abscissa or the root radius of a monic polynomial family with a single affine constraint on its coefficients)
  
  
• SDPpack: a package for Semidefinite Programming

Optimization Benchmarking

• betaRMP: beta-Relative Minimization Profiles
  (benchmarking visualization tool for creating plots that concisely compare optimization methods evaluated on large heterogenous sets of test problems, written by Tim Mitchell)
  
  
• PSARNOT: (Pseudo)Spectral Abscissa|Radius Nonsmooth Optimization Test
  (a test set for evaluating methods for nonsmooth optimization, written by Tim Mitchell)

Matrix Functions

• Generalized Null Space Decomposition
  (this decomposition, also known as the Staircase Form, can be used to identify the Jordan block structure for the zero eigenvalues of a matrix. It can also be used to compute the Drazin inverse)
  
  
• ROSTAPACK: RObust STAbility PACKage
  (for many robust stabilization measures for matrices and linear dynamical systems. This package, written by Tim Mitchell, greatly extends, improves upon and replaces our earlier algorithms and codes for the pseudospectral abscissa and radius, both the criss-cross method (use the new code specValSet), and the faster methods for large sparse problems (use the new code specValSetBound))
  
  
• Distance to Uncontrollability
  
  
• Sep-Lambda
  
  
• Nearest Defective Matrix