Constraint function
A constraint function is a function whose value expresses whether decision variables satisfy a feasibility restriction in an optimization problem.
Optimization Algorithms: AI techniques for design, planning, and control problems
A constraint function is a function that expresses a feasibility restriction on the values of decision variables in an optimization problem.
- How it is used
- Frames feasibility restrictions that keep optimization decisions within permitted limits.
- How deep it goes
- Explains inequality constraints, Lagrangian reformulation, derivative equations, and a SymPy implementation.
- Examples
- Uses a 10,000-ticket capacity limit and a physical-versus-virtual ticket allocation problem.
- What you can do after
- Apply it via SymPy to formulate and solve a constrained optimization problem with a Lagrangian.
Bayesian Optimization in Action
A constraint function is a function whose value determines whether a candidate satisfies a specified optimization constraint.
- How it is used
- Guides Bayesian optimization toward candidates that improve an objective while satisfying black-box constraints.
- How deep it goes
- Defines black-box modeling and probabilistic feasibility, but does not detail Gaussian-process internals.
- Examples
- Uses a black-box cost function whose value must be nonpositive as the constraint example.
- What you can do after
- Apply constrained expected improvement with objective and constraint Gaussian processes in BoTorch.
Read how Bayesian Optimization in Action explains constraint function →
Related concepts
- Gaussian processuses · A Gaussian process is a probability distribution over functions in which every finite collection of function values has a joint Gaussian distribution.
- black-box solverused by · A black-box solver optimizes an objective through input-output evaluations without requiring access to its internal analytical form or dynamics.
- objective functionproduces · An objective function is a mathematical function or criterion that assigns values to candidate solutions or parameter settings and is optimized toward a specified goal.
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