Mathematics and Optimization

Develop, solve, and visualize mathematical models

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 using patternsearch or ga.

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

Discretized Optimal Trajectory, Problem-Based

Solve a discretized optimal trajectory problem using the problem-based approach.

(Optimization Toolbox)

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.

(Global Optimization Toolbox)

Visualize Aircraft Line-of-Sight over Terrain

Compute and visualize line-of-sight visibility of an aircraft from a ground location over terrain.

(Mapping Toolbox)

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.

(Mapping Toolbox)

Since R2023b

Battery Module Cooling Analysis and Reduced-Order Thermal Model

Perform a battery cooling analysis to determine effect of a cooling system.

(Partial Differential Equation Toolbox)