Package dev.nm.solver.multivariate.constrained

Constrained minimization: translating a mathematical problem into solver inputs.

See: Description

Interface Summary

Interface	Description
BoxMinimizer<P extends BoxOptimProblem,S extends MinimizationSolution<?>>	A box minimizer solves a BoxOptimProblem.
ConstrainedMinimizer<P extends ConstrainedOptimProblem,S extends MinimizationSolution<?>>	A constrained minimizer solves a constrained optimization problem, namely, ConstrainedOptimProblem.
ConstrainedOptimSubProblem	A constrained optimization sub-problem takes this form. \[ \min_x f(x) \] s.t., {x_i = v_i}, for some i's, i.e., some values of x are fixed hi(x) = 0 gi(x) ≤ 0 This representations is simply the union of the original optimization problem and the fixed values.
SubProblemMinimizer.ConstrainedMinimizerFactory<U extends ConstrainedMinimizer<ConstrainedOptimProblem,IterativeSolution<Vector>>>	This factory constructs a new instance of ConstrainedMinimizer to solve a real valued minimization problem.
SubProblemMinimizer.IterativeSolution<Vector>

Class Summary

Class	Description
SubProblemMinimizer	This minimizer solves a constrained optimization sub-problem where the values for some variables are held fixed for the original optimization problem.

Package dev.nm.solver.multivariate.constrained Description

Constrained minimization: translating a mathematical problem into solver inputs.

Choose the simplest matching solver

• A convex quadratic objective with linear constraints: construct QPProblem and use a QP minimizer. The active-set example checks a binding budget.
• A smooth nonlinear objective or nonlinear constraints: see SQPActiveSetMinimizer for an iterative local SQP method. Local search does not promise a global optimum.

Translate signs, dimensions and scales

An equality residual is zero. A LessThanConstraints residual is at most zero. Linear wrappers instead take A and b with the direction stated by the class: \(Ax\leq b\) or \(Ax\geq b\). Negate both sides to switch direction. The quadratic convention is \(\tfrac12 x^{\mathsf T}Hx+p^{\mathsf T}x\).

One matrix row represents one constraint; columns represent variables in the same order used by the objective. Select tolerances after scaling variables and residuals to meaningful units. A raw step-size threshold is not a relative-error guarantee on every variable or objective value.

Run and verify

1. Prepare a dimensionally consistent objective and constraint collection.
2. Call solve(problem) to create a solution/search object.
3. Provide the initial values required by that solver, or use an explicitly supported feasible-point search overload.
4. After search, recompute the objective, equality residuals and inequality violations in the original units. Check the solver's exception/stopping contract.

SQP expects a feasible starting point; a QP explicit-start overload can require strict feasibility. Do not silently reuse a prior solution after an exception, or treat reaching an iteration budget as an optimality certificate.