Quadratic program

As explained in Machine Learning Algorithms in Depth

A quadratic program is an optimization problem with a quadratic objective function and linear constraints on its variables.

Optimizes a quadratic objective subject to linear constraints on variables. In support vector machines, minimizing the squared norm of the parameter vector under correct-classification constraints maximizes the geometric margin. section 5.3

The SVM formulation connects the quadratic program to several equivalent views:

• The primal minimizes a regularized loss or parameter norm while enforcing classification constraints. section 5.3
• The dual reverses optimization direction, turning primal variables into constraints and primal constraints into variables. section 5.3
• The Lagrangian provides the route from the primal formulation to the dual. section 5.3

Maximum-margin SVM

Training pushes the margin boundaries apart until another classification constraint would be violated. Points on those boundaries become support vectors, and only this subset is needed to determine the SVM parameters. section 5.3

Figure 5.8 Max margin solution of SVM classifier

Use the maximum-margin diagram to relate the quadratic objective, classification constraints, margin boundaries, and support vectors. section 5.3

How Machine Learning Algorithms in Depth covers it

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.

How it connects

Connects quadratic programs to support vector machines, maximum margin, regularization, Lagrangians, and duality.

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Also explained in

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  Optimization Algorithms: AI techniques for design, planning, and control problemsQuadratic programming is optimization with a quadratic objective function and typically linear constraints.

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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.

This explainer was generated by Manning's knowledge graph from the text of Machine Learning Algorithms in Depth. The section links point to the parts of the book it draws on.