Solve problems with quadratic objectives and linear
constraints

Before you begin to solve an optimization problem, you must choose the appropriate approach: problem-based or solver-based. For details, see First Choose Problem-Based or Solver-Based Approach.

For the problem-based approach, create problem variables, and then
represent the objective function and constraints in terms of these symbolic
variables. For the problem-based steps to take, see Problem-Based Optimization Workflow. To
solve the resulting problem, use `solve`

.

For the solver-based steps to take, including defining the objective
function and constraints, and choosing the appropriate solver, see Solver-Based Optimization Problem Setup. To solve the
resulting problem, use `quadprog`

.

**Quadratic Programming with Bound Constraints: Problem-Based**

Shows how to solve a problem-based quadratic programming problem with bound constraints using different algorithms.

**Large Sparse Quadratic Program, Problem-Based**

Shows how to solve a large sparse quadratic program using the problem-based approach.

**Bound-Constrained Quadratic Programming, Problem-Based**

Example showing large-scale problem-based quadratic programming.

**Quadratic Programming for Portfolio Optimization, Problem-Based**

Example showing problem-based quadratic programming on a basic portfolio model.

**Quadratic Minimization with Bound Constraints**

Example of quadratic programming with bound constraints.

**Quadratic Programming with Many Linear Constraints**

This example shows the benefit of the active-set algorithm on problems with many linear constraints.

**Quadratic Minimization with Dense, Structured Hessian**

Example showing how to save memory in a structured quadratic program.

**Large Sparse Quadratic Program with Interior Point Algorithm**

Example showing how to save memory in a quadratic program by using a sparse quadratic matrix.

**Bound-Constrained Quadratic Programming, Solver-Based**

Example showing solver-based large-scale quadratic programming.

**Quadratic Programming for Portfolio Optimization Problems, Solver-Based**

Example showing solver-based quadratic programming on a basic portfolio model.

Generate C code for quadratic optimization.

Learn the basics of code generation for the `quadprog`

optimization solver.

**Optimization Code Generation for Real-Time Applications**

Explore techniques for handling real-time requirements in generated code.

**Problem-Based Optimization Algorithms**

How the optimization functions and objects solve optimization problems.

**Supported Operations on Optimization Variables and Expressions**

Lists all available mathematical and indexing operations on optimization variables and expressions.

**Quadratic Programming Algorithms**

Minimizing a quadratic objective function in *n* dimensions
with only linear and bound constraints.

**Optimization Options Reference**

Explore optimization options.