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It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.<br><br>Here are some common dental emergencies:<br>Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.<br><br>At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.<br><br>Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.<br><br>Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.<br><br>Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.<br><br>Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.<br><br>Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.<br><br>In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.<br><br>If you have any sort of questions regarding where and just how to utilize [http://www.youtube.com/watch?v=90z1mmiwNS8 Dentists in DC], you could contact us at our own website.
:''"Active Set" redirects here. For the Wikipedia article on the band, see [[The Active Set]].''
 
In [[Optimization (mathematics)|optimization]], a problem is defined using an objective function to minimize or maximize, and a set of constraints
 
:<math>g_1(x)\ge 0, \dots, g_k(x)\ge 0</math>  
 
that define the [[feasible region]], that is, the set of all ''x'' to search for the optimal solution. Given a point <math>x</math> in the feasible region, a constraint
:<math>g_i(x) \ge 0</math>
is called '''active''' at <math>x</math> if <math>g_i(x)=0</math> and '''inactive''' at <math>x</math> if <math>g_i(x)>0.</math> Equality constraints are always active. The '''active set''' at <math>x</math> is made up of those constraints <math>g_i(x)</math> that are active at the current point {{harv|Nocedal|Wright|2006|p=308}}.
 
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''' include{{Citation needed|date=November 2013}}:
* [[Successive linear programming]] (SLP) <!-- acc. to: Leyffer... - alt: acc. to "MPS glossary", http://glossary.computing.society.informs.org/ver2/mpgwiki/index.php/Main_Page: Successive approximation -->
* [[Sequential quadratic programming]] (SQP) <!-- acc. to: Leyffer... - alt: acc. to "MPS glossary", http://glossary.computing.society.informs.org/ver2/mpgwiki/index.php/Main_Page: Successive approximation  -->
* [[Sequential linear-quadratic programming]] (SLQP) <!-- acc. to: Leyffer... - alt: acc. to "MPS glossary", http://glossary.computing.society.informs.org/ver2/mpgwiki/index.php/Main_Page: Successive approximation  -->
* [[Frank–Wolfe algorithm|Reduced gradient method]] (RG) <!-- acc. to: MPS glossary, http://glossary.computing.society.informs.org/ver2/mpgwiki/index.php/Main_Page - alt: acc. to "Optimization - Theory and Practice" (Forst, Hoffmann): Projection method -->
* [[Generalized Reduced Gradient|Generalized Reduced Gradient method]] (GRG) <!-- acc. to: MPS glossary, http://glossary.computing.society.informs.org/ver2/mpgwiki/index.php/Main_Page - alt: acc. to "Optimization - Theory and Practice" (Forst, Hoffmann): Projection method -->
<!-- ? Wilson's Lagrange-newton method -->
<!-- ? Method of feasible directions (MFD) -->
<!-- ? Gradient projection method -  alt: acc. to "Optimization - Theory and Practice" (Forst, Hoffmann): Projection method -->
 
==References==
* {{cite book|last=Murty|first=K. G.|title=Linear complementarity, linear and nonlinear programming|series=Sigma Series in Applied Mathematics|volume=3|publisher=Heldermann Verlag|location=Berlin|year=1988|pages=xlviii+629 pp.|isbn=3-88538-403-5|url=http://ioe.engin.umich.edu/people/fac/books/murty/linear_complementarity_webbook/}} {{MR|949214}}
* {{Cite book | last1=Nocedal | first1=Jorge | last2=Wright | first2=Stephen J. | title=Numerical Optimization | publisher=[[Springer-Verlag]] | location=Berlin, New York | edition=2nd | isbn=978-0-387-30303-1 | year=2006 | ref=harv | postscript=<!--None-->}}.
 
 
[[Category:Mathematical optimization]]
[[Category:Optimization algorithms and methods]]

Revision as of 03:54, 27 July 2013

"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

g1(x)≥0,…,gk(x)≥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

gi(x)≥0

is called active at x if gi(x)=0 and inactive at x if gi(x)>0. Equality constraints are always active. The active set at x is made up of those constraints gi(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.:

References

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