Search results
Results from the WOW.Com Content Network
The Lagrange multiplier theorem states that at any local maximum (or minimum) of the function evaluated under the equality constraints, if constraint qualification applies (explained below), then the gradient of the function (at that point) can be expressed as a linear combination of the gradients of the constraints (at that point), with the ...
Augmented Lagrangian methods are a certain class of algorithms for solving constrained optimization problems. They have similarities to penalty methods in that they replace a constrained optimization problem by a series of unconstrained problems and add a penalty term to the objective, but the augmented Lagrangian method adds yet another term designed to mimic a Lagrange multiplier.
A practical way to enforce this is by requiring that the next search direction be built out of the current residual and all previous search directions. The conjugation constraint is an orthonormal-type constraint and hence the algorithm can be viewed as an example of Gram-Schmidt orthonormalization. This gives the following expression:
Various kinds of local consistency conditions are leveraged, including node consistency, arc consistency, and path consistency. Every local consistency condition can be enforced by a transformation that changes the problem without changing its solutions; such a transformation is called constraint propagation. Constraint propagation works by ...
Consider the following nonlinear optimization problem in standard form: . minimize () subject to (),() =where is the optimization variable chosen from a convex subset of , is the objective or utility function, (=, …,) are the inequality constraint functions and (=, …,) are the equality constraint functions.
The overall result is that when one ant finds a good (i.e., short) path from the colony to a food source, other ants are more likely to follow that path, and positive feedback eventually leads to many ants following a single path. The idea of the ant colony algorithm is to mimic this behavior with "simulated ants" walking around the graph ...
In typed lambda calculus, functions can be applied only if they are capable of accepting the given input's "type" of data. Typed lambda calculi are strictly weaker than the untyped lambda calculus, which is the primary subject of this article, in the sense that typed lambda calculi can express less than the untyped calculus can. On the other ...
The primary application of the Levenberg–Marquardt algorithm is in the least-squares curve fitting problem: given a set of empirical pairs (,) of independent and dependent variables, find the parameters of the model curve (,) so that the sum of the squares of the deviations () is minimized: