Quadratic program
A quadratic program is an optimization problem with a quadratic objective function and linear constraints on its variables.
Optimization Algorithms: AI techniques for design, planning, and control problems
Quadratic programming is optimization with a quadratic objective function and typically linear constraints.
- How it is used
- Frames assignment and layout decisions where quadratic costs capture interactions between facilities, flows, and distances.
- How deep it goes
- Defines quadratic objectives and gives a matrix formulation, but does not develop a QP-solving algorithm or implementation.
- Examples
- Uses plant layout and facility location, with flow and distance matrices representing material-handling costs.
- What you can do after
- Evaluate/understand how facility assignments become quadratic objectives involving flows, distances, and matrix products.
Machine Learning Algorithms in Depth
A quadratic program is an optimization problem with a quadratic objective function and linear constraints on its variables.
- How it is used
- Formulates maximum-margin support vector machine training as constrained optimization.
- How deep it goes
- Explains the objective, constraints, margin geometry, and primal-dual correspondence, then points toward Lagrangian derivation.
- Examples
- Uses maximum-margin geometry, support vectors, SVM pseudocode, and an Iris classification implementation.
- What you can do after
- Apply quadratic programming through an SVM implementation using cvxopt or scikit-learn's SVC.
Read how Machine Learning Algorithms in Depth explains quadratic program →
Related concepts
- nonlinear programmingkind of · Nonlinear programming is optimization in which the objective function or at least one constraint is nonlinear.
- CVXOPTused by · CVXOPT is a Python software package for convex optimization, including quadratic programming.
- support vector machineused by · A support vector machine is a supervised-learning model that uses support vectors to determine a maximum-margin decision boundary or regression function, optionally using kernels to model nonlinear relationships.
- quadratic assignment problemincludes · A quadratic assignment problem assigns facilities to locations while minimizing interaction flow weighted by assigned-location distances.
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