Typographical Conventions This manual uses some or all of these conventions ltem Conventi。n Example Example code Monospace font To assign the value 5 to a Function names, syntax Monospace font The cos function finds the filenames, directory/folder cosine of each array element names, and user input Syntax line example is MLGetVar ML var name Buttons and keys Boldface with book title caps Press the Enter key. Literal strings(in syntax Monospace bold for literals f freespace(n, ' whole') descriptions in reference Mathematical Italics for variables This vector represents the expressions Standard text font for functions, polynomial p=x2+ 2x+3 operators, and constants MATLAB Monospace font MATLAB responds with Menu and dialog box titles Boldface with book title caps Choose the File Options New terms and for Italics An array is an ordered collection of information Omitted input arguments (ellipsis denotes all of the [c, ia, ib]= union input/output arguments from preceding syntaxes String variables(from a Monospace italics sysc d2c sysd, method ') finite list)
Typographical Conventions xi Typographical Conventions This manual uses some or all of these conventions. Item Convention Example Example code Monospace font To assign the value 5 to A, enter A = 5 Function names, syntax, filenames, directory/folder names, and user input Monospace font The cos function finds the cosine of each array element. Syntax line example is MLGetVar ML_var_name Buttons and keys Boldface with book title caps Press the Enter key. Literal strings (in syntax descriptions in reference chapters) Monospace bold for literals f = freqspace(n,'whole') Mathematical expressions Italics for variables Standard text font for functions, operators, and constants This vector represents the polynomial p = x2 + 2x + 3. MATLAB output Monospace font MATLAB responds with A = 5 Menu and dialog box titles Boldface with book title caps Choose the File Options menu. New terms and for emphasis Italics An array is an ordered collection of information. Omitted input arguments (...) ellipsis denotes all of the input/output arguments from preceding syntaxes. [c,ia,ib] = union(...) String variables (from a finite list) Monospace italics sysc = d2c(sysd,'method')
Introduction The Introduction consists of these sections What Is the Optimization Toolbox?(p. 1-2) Introduces the Optimization Toolbox, and describes its intended use and its capabilities New Features in Version 2.2(p. 1-3) Introduces features that are new in version 2.2 Configuration Information(p. 1-4) Directs you to installation and configuration information Technical Conventions (p. 1-5) Describes mathematical notation used in this guide Acknowledgments(p 1-6) Acknowledges significant contributions to the Optimization toolbox
1 Introduction The Introduction consists of these sections: What Is the Optimization Toolbox? (p. 1-2) Introduces the Optimization Toolbox, and describes its intended use and its capabilities. New Features in Version 2.2 (p. 1-3) Introduces features that are new in Version 2.2. Configuration Information (p. 1-4) Directs you to installation and configuration information. Technical Conventions (p. 1-5) Describes mathematical notation used in this guide. Acknowledgments (p. 1-6) Acknowledges significant contributions to the Optimization Toolbox
Introduction What Is the Optimization Toolbox? The Optimization Toolbox is a collection of functions that extend the capability of the MATLAB@ numeric computing environment. The toolbox includes routines for many types of optimization including Unconstrained nonlinear minimization Constrained nonlinear minimization, including goal attainment problems minimax problems, and semi-infinite minimization problems Quadratic and linear programming Nonlinear system of equation solving Constrained linear least squares Sparse and structured large-scale problems All the toolbox functions are MATLAB M-files, made up of matLAB statements that implement specialized optimization algorithms. You can view the matlAb code for these functions using the statement type functie You can extend the capabilities of the Optimization Toolbox by writing your own M-files, or by using the toolbox in combination with other toolboxes, or with matLab or Simulink 1-2
1 Introduction 1-2 What Is the Optimization Toolbox? The Optimization Toolbox is a collection of functions that extend the capability of the MATLAB® numeric computing environment. The toolbox includes routines for many types of optimization including • Unconstrained nonlinear minimization • Constrained nonlinear minimization, including goal attainment problems, minimax problems, and semi-infinite minimization problems • Quadratic and linear programming • Nonlinear least squares and curve-fitting • Nonlinear system of equation solving • Constrained linear least squares • Sparse and structured large-scale problems All the toolbox functions are MATLAB M-files, made up of MATLAB statements that implement specialized optimization algorithms. You can view the MATLAB code for these functions using the statement type function_name You can extend the capabilities of the Optimization Toolbox by writing your own M-files, or by using the toolbox in combination with other toolboxes, or with MATLAB or Simulink®
New Fe Version 2.2 New Features in version 2.2 Version 2.2 (Beta 2)of the Optimization Toolbox offers a"New fsolve Default New fsolve Default Algorithm The fsolve function, which is used to solve systems of nonlinear equations, has a new default algorithm for medium-scale systems where the number of equations is equal to the number of variables. The new algorithm uses a trust-region dogleg method that has improved convergence properties over the previous default method. In keeping with the new default trust-region dogleg algorithm, fsolve now defaults to the medium-scale method. A new NonlEqnAlgorithm'fsolve parameter enables you to choose the Levenberg- Marquardt or Gauss-Newton algorithm over the trust-region dogleg algorith For more information, see"Nonlinear Systems of Equations"on page 3-24 "Nonlinear Equations Implementation"on page 3-26, and the fsolve reference page
New Features in Version 2.2 1-3 New Features in Version 2.2 Version 2.2 (Beta 2) of the Optimization Toolbox offers a “New fsolve Default Algorithm” New fsolve Default Algorithm The fsolve function, which is used to solve systems of nonlinear equations, has a new default algorithm for medium-scale systems where the number of equations is equal to the number of variables. The new algorithm uses a trust-region dogleg method that has improved convergence properties over the previous default method. In keeping with the new default trust-region dogleg algorithm, fsolve now defaults to the medium-scale method. A new 'NonlEqnAlgorithm' fsolve parameter enables you to choose the Levenberg-Marquardt or Gauss-Newton algorithm over the trust-region dogleg algorithm. For more information, see “Nonlinear Systems of Equations” on page 3-24, “Nonlinear Equations Implementation” on page 3-26, and the fsolve reference page
Introduction Configuration Information determine whether the Optimization Toolbox is installed on your system type this command at the matlaB prompt When you enter this command, MatLAB displays information about the version of MATLAB you are running, including a list of all toolboxes installed on your system and their version numbers If the Optimization Toolbox is not installed, check the Installation documentation for your platform for instructions on how to install it. Note For the most up-to-date information about system requirements, see the individual product pages at the Math Works Web site (http://www.mathworks.com) 1-4
1 Introduction 1-4 Configuration Information To determine whether the Optimization Toolbox is installed on your system, type this command at the MATLAB prompt. ver When you enter this command, MATLAB displays information about the version of MATLAB you are running, including a list of all toolboxes installed on your system and their version numbers. If the Optimization Toolbox is not installed, check the Installation documentation for your platform for instructions on how to install it. Note For the most up-to-date information about system requirements, see the individual product pages at the MathWorks Web site (http://www.mathworks.com)