gtsam 4.1.1
gtsam

Policy for ActivetSetSolver to solve Linear Programming.
Static Public Member Functions  
static GaussianFactorGraph  buildCostFunction (const LP &lp, const VectorValues &xk) 
Create the factor xxk  (g)^2 where xk is the current feasible solution on the constraint surface and g is the gradient of the linear cost, i.e. More...  
Static Public Attributes  
static constexpr double  maxAlpha = std::numeric_limits<double>::infinity() 
Maximum alpha for line search x'=xk + alpha*p, where p is the cost gradient For LP, maxAlpha = Infinity.  

inlinestatic 
Create the factor xxk  (g)^2 where xk is the current feasible solution on the constraint surface and g is the gradient of the linear cost, i.e.
g is the direction we wish to follow to decrease the cost.
Essentially, we try to match the direction d = xxk with g as much as possible subject to the condition that x needs to be on the constraint surface, i.e., d is along the surface's subspace.
The leastsquare solution of this quadratic subject to a set of linear constraints is the projection of the gradient onto the constraints' subspace