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Fixed up comments

release/4.3a0
dellaert 2014-11-26 22:59:33 +01:00
parent ad07531453
commit ba911edfad
1 changed files with 15 additions and 14 deletions
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29
gtsam_unstable/linear/QPSolver.h
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@ -78,31 +78,32 @@ public:
const VectorValues& x0, bool useLeastSquare = false) const;
/**
* Find the BAD active ineq that pulls x strongest to the wrong direction of its constraint
* (i.e. it is pulling towards >0, while its feasible region is <=0)
* Find the BAD active inequality that pulls x strongest to the wrong direction
* of its constraint (i.e. it is pulling towards >0, while its feasible region is <=0)
*
* For active ineq constraints (those that are enforced as eq constraints now
* in the working set), we want lambda < 0.
* For active inequality constraints (those that are enforced as equality constraints
* in the current working set), we want lambda < 0.
* This is because:
* - From the Lagrangian L = f - lambda*c, we know that the constraint force is
* (lambda * \grad c) = \grad f, because it cancels out the unconstrained
* unconstrained force (-\grad f), which is pulling x in the opposite direction
* of \grad f towards the unconstrained minimum point
* - We also know that at the constraint surface \grad c points toward + (>= 0),
* - From the Lagrangian L = f - lambda*c, we know that the constraint force
* is (lambda * \grad c) = \grad f, because it cancels out the unconstrained
* force (-\grad f), which is pulling x in the opposite direction of \grad f
* towards the unconstrained minimum point
* - We also know that at the constraint surface \grad c points toward + (>= 0),
* while we are solving for - (<=0) constraint
* - So, we want the constraint force (lambda * \grad c) to to pull x
* - So, we want the constraint force (lambda * \grad c) to to pull x
* towards the opposite direction of \grad c, i.e. towards the area
* where the ineq constraint <=0 is satisfied.
* - Hence, we want lambda < 0
* where the inequality constraint <=0 is satisfied.
* - Hence, we want lambda < 0
*
* So active ineqs with lambda > 0 are BAD. And we want the worst one with the largest lambda.
* So active inequality constraints with lambda > 0 are BAD.
* And we want the worst one with the largest lambda.
*
*/
std::pair<int, int> findWorstViolatedActiveIneq(
const VectorValues& lambdas) const;
/**
* Deactivate or activate an ineq constraint in place
* Deactivate or activate an inequality constraint in place
* Warning: modify in-place to avoid copy/clone
* @return true if update successful
*/