Mean motion

"Active Set" redirects here. For the Wikipedia article on the band, see The Active Set.

In optimization, a problem is defined using an objective function to minimize or maximize, and a set of constraints

$g_{1}(x)\geq 0,\dots ,g_{k}(x)\geq 0$

that define the feasible region, that is, the set of all x to search for the optimal solution. Given a point $x$ in the feasible region, a constraint

$g_{i}(x)\geq 0$

is called active at $x$ if $g_{i}(x)=0$ and inactive at $x$ if $g_{i}(x)>0.$ Equality constraints are always active. The active set at $x$ is made up of those constraints $g_{i}(x)$ that are active at the current point Template:Harv.

The active set is particularly important in optimization theory as it determines which constraints will influence the final result of optimization. For example, in solving the linear programming problem, the active set gives the hyperplanes that intersect at the solution point. In quadratic programming, as the solution is not necessarily on one of the edges of the bounding polygon, an estimation of the active set gives us a subset of inequalities to watch while searching the solution, which reduces the complexity of the search.

Active set methods

In general an active set algorithm has the following structure:

Find a feasible starting point

repeat until "optimal enough"

solve the equality problem defined by the active set (approximately)

compute the Lagrange multipliers of the active set

remove a subset of the constraints with negative Lagrange multipliers

search for infeasible constraints

end repeat

Methods that can be described as active set methods includePotter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.:

• Successive linear programming (SLP)
• Sequential quadratic programming (SQP)
• Sequential linear-quadratic programming (SLQP)
• Reduced gradient method (RG)
• Generalized Reduced Gradient method (GRG)

References

• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 Template:MR
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534.