Mathematics and Optimization
Several MATLAB® products can help you to create and analyze mathematical models. These products offer multiple modeling approaches that include core and specialized mathematical tools, numeric and symbolic computation, and interactive and programmatic functionality.
Products for Mathematics and Optimization
Optimization Toolbox
Solve linear, quadratic, conic, integer, and nonlinear optimization problems
Global Optimization Toolbox
Solve multiple maxima, multiple minima, and nonsmooth optimization problems
Symbolic Math Toolbox
Perform symbolic math computations
Mapping Toolbox
Analyze and visualize geographic information
Partial Differential Equation Toolbox
Solve partial differential equations using finite element analysis
Topics
Optimization
- Constrained Nonlinear Problem Using Optimize Live Editor Task or Solver (Optimization Toolbox)
Minimize a nonlinear function with a nonlinear constraint using a visual approach or a text-based approach. - Constrained Electrostatic Nonlinear Optimization Using Optimization Variables (Optimization Toolbox)
Define objective and constraint functions for a structured nonlinear optimization in the problem-based approach. - Fit ODE Parameters Using Optimization Variables (Optimization Toolbox)
Fit parameters of an ODE using problem-based least squares.
Global Optimization
- Comparison of Six Solvers (Global Optimization Toolbox)
Explore some characteristics of global solvers. - Solve Nonlinear Problem with Integer and Nonlinear Constraints (Global Optimization Toolbox)
Compare the solution of a nonlinear problem both with and without integer constraints. - Optimize ODEs in Parallel (Global Optimization Toolbox)
Save time by calling an expensive subroutine just once and computing an ODE solution in parallel usingpatternsearchorga.
Symbolic Math
- Create Symbolic Numbers, Variables, and Expressions (Symbolic Math Toolbox)
Use symbolic values and variables to perform analytical calculations. - Differentiation (Symbolic Math Toolbox)
Differentiate symbolic expressions and functions. - Integration (Symbolic Math Toolbox)
Integrate symbolic expressions and functions.
Mapping
- Choose a 2-D Map Display (Mapping Toolbox)
Choose a 2-D map display based on criteria such as the map projection, the type of data, and interactivity options. - Supported Geospatial File Formats for Import and Export (Mapping Toolbox)
File formats that Mapping Toolbox™ can read and write, and recommended functions. - Comparison of 3-D Coordinate Systems (Mapping Toolbox)
Learn how to choose a coordinate transformation function based on your data.
Partial Differential Equations
- Deflection Analysis of Bracket (Partial Differential Equation Toolbox)
Analyze a bracket under an applied load and determine the maximal deflection by using the unified workflow. - Heat Transfer in Block with Cavity (Partial Differential Equation Toolbox)
Find the heat distribution in a block with a cavity by using the unified workflow. - Electrostatic Potential in Air-Filled Frame (Partial Differential Equation Toolbox)
Find the electrostatic potential in an air-filled annular quadrilateral frame by using the unified workflow.
Featured Examples
Use Optimization Explorer App
Basic example showing the use of the Optimization Explorer App.
Plan Nuclear Fuel Disposal Using Multiobjective Optimization
Plan the disposal of spent nuclear fuel while minimizing both cost and risks. This example has both continuous and binary variables.
Visualize Aircraft Line-of-Sight over Terrain
Compute and visualize line-of-sight visibility of an aircraft from a ground location over terrain.
Visualize Sea Ice Concentrations from GRIB Data
Read sea ice concentrations from a GRIB file and visualize the data using a 2-D map, an animated GIF, and histograms.
Battery Module Cooling Analysis and Reduced-Order Thermal Model
Perform a battery cooling analysis to determine effect of a cooling system.
Model Battery Performance
Simulate the battery discharge with a dynamic current profile and battery charging with a constant current. Incorporate the Arrhenius temperature correction on diffusion coefficients and ionic conductivity.
Videos
What Is Optimization Toolbox?
Optimization Toolbox™ provides functions for finding parameters that minimize or
maximize objectives while satisfying constraints.
