Linked from

The 37 pages that link to Lagrange multiplier, each with the reason it gives.

• Joseph-Louis LagrangeBroader topic: The method turns constrained optimization into equations involving auxiliary variables.

• Partial derivativeBroader topic: The method turns partial-derivative conditions into equations for constrained optima.

• Calculus of variationsCompared with: Finite-dimensional multipliers have a direct analogue in constrained variational problems.

• Convex optimizationRelated: Multipliers encode how constraints affect optimality and sensitivity.

• Euler–Lagrange EquationCompared with: It handles finite-dimensional constrained extrema, unlike the differential condition for function-valued inputs.

• Dual spaceRelated: Constraint gradients act as covectors that combine to balance an objective's derivative.

• Constrained optimizationRelated: At a smooth constrained optimum, the objective gradient can align with constraint gradients through these multipliers.

• Implicit function theoremRelated: The theorem helps justify local dependence of constrained stationary points on parameters.

• Generalized coordinatesRelated: They let constrained motion be formulated without eliminating every dependent coordinate.

• Comparative staticsRelated: Its parameter response helps interpret changing constraints in comparative statics.

• Linear programming dualityRelated: Dual variables act as multipliers on primal constraints.

• Hahn–Banach theoremCompared with: Unlike this optimization tool, Hahn–Banach derives separating functionals from linear extension.

• Mathematical economicsBroader topic: It turns economic constraints into conditions that can be analyzed algebraically.

• D'Alembert's principleRelated: They let constrained equations of motion retain constraint forces instead of eliminating them.

• Economic dispatchRelated: The multiplier on the demand balance represents the system’s marginal cost of supplying more power.

• Karush–Kuhn–Tucker conditionsRelated: KKT conditions extend multiplier methods to inequality constraints.

• Neumann boundary conditionRelated: Multiplier formulations can enforce prescribed boundary data in finite-element problems.

• Equality conditionRelated: Optimization proofs often derive equality cases by solving the associated stationarity conditions.

• Geometric inequalityRelated: It identifies candidate extremal shapes when geometric measurements are fixed.

• Linear functionalRelated: Constraint derivatives act as functionals that shape optimality conditions.

• Isoperimetric problemRelated: It enforces the integral constraint while deriving necessary conditions for an extremum.

• Optimization problemRelated: It turns constrained optimality into equations involving objective and constraint gradients.

• Shadow priceRelated: In smooth problems, the multiplier often equals the constraint’s shadow price, up to sign convention.

• Constraint (mechanics)Related: In constrained mechanics, it often represents the strength of a constraint force.

• Maximum and minimumRelated: At constrained interior extrema, gradients of the objective and constraints satisfy a proportionality condition.

• Nonlinear programmingRelated: They turn active constraints into terms in nonlinear programming's first-order conditions.

• Envelope theoremRelated: With constraints, multipliers enter the envelope formula through the Lagrangian.

• Implicit functionRelated: Equality constraints are implicit relations that shape the feasible set.

• Multivariable calculusBroader topic: It turns constrained optimization into equations involving gradients.

• Hadwiger–Finsler inequalityRelated: Optimization under fixed side-length measures can recover the equilateral equality case.

• Karamata's inequalityCompared with: Optimization can prove some symmetric bounds, while Karamata gives a direct order-based comparison.

• Virtual workRelated: They can encode constraint forces when deriving equilibrium from virtual work.

• Multibody systemRelated: In constrained dynamics they represent forces associated with ideal constraints.

• Function of several real variablesRelated: It links gradients of an objective and its constraints at candidate extrema.

• Interior extremum theoremRelated: Constrained optimization replaces the unconstrained zero-gradient condition with a constraint relation.

• Pontryagin's maximum principleRelated: Costates play a related multiplier role for the system's differential constraints.

• Principle of minimum energyRelated: It converts constrained energy minimization into equations for candidate equilibria.