First Choose Problem-Based or Solver-Based Approach

Optimization Toolbox™ has two approaches to solving optimization problems or equations: problem-based and solver-based. Before you start to solve a problem, you must first choose the appropriate approach.

This table summarizes the main differences between the two approaches.

Approaches	Characteristics
Problem-Based Optimization Setup	Easier to create and debug
	Provides a visual interface; see Optimize Live Editor task
	Represents the objective and constraints symbolically
	Requires translation from problem form to matrix form, potentially resulting in a longer solution time
	Automatically calculates and uses gradients of objective and nonlinear constraint functions in many cases, but does not calculate Hessians; see Automatic Differentiation
	See the steps in Problem-Based Optimization Workflow or Problem-Based Workflow for Solving Equations
	Basic linear example: Mixed-Integer Linear Programming Basics: Problem-Based or the video Solve a Mixed-Integer Linear Programming Problem using Optimization Modeling Basic nonlinear example: Solve a Constrained Nonlinear Problem, Problem-Based Basic equation-solving example: Solve Nonlinear System of Equations, Problem-Based
Solver-Based Optimization Problem Setup	Harder to create and debug
	Provides a visual interface; see Optimize Live Editor task
	Represents the objective and constraints as functions or matrices
	Does not require translation from problem form to matrix form, potentially resulting in a shorter solution time
	Allows direct inclusion of gradient or Hessian, but does not calculate them automatically
	Allows use of a Hessian multiply function or Jacobian multiply function to save memory in large problems See Quadratic Minimization with Dense, Structured Hessian or Jacobian Multiply Function with Linear Least Squares
	See the steps in Solver-Based Optimization Problem Setup
	Basic linear example: Mixed-Integer Linear Programming Basics: Solver-Based Basic nonlinear example: Constrained Nonlinear Problem Using Optimize Live Editor Task or Solver Basic equation-solving examples: Examples