QuadraticMinimizer
Related Docs:
object QuadraticMinimizer
| package proximal
rank of dense gram matrix
proximal operator to be used
rhs matrix for equality constraints
lhs constants for equality constraints
ADMM absolute tolerance
ADMM relative tolerance
over-relaxation parameter default 1.0 1.5 - 1.8 can improve convergence
Public API to get an initialState for solver hot start such that subsequent calls can reuse state memmory
Public API to get an initialState for solver hot start such that subsequent calls can reuse state memmory
the state for the optimizer
minimize API for cases where upper triangular gram matrix is provided by user as primitive array.
minimize API for cases where upper triangular gram matrix is provided by user as primitive array. If a initialState is not provided by default it constructs it through initialize
upper triangular gram matrix of size rank x (rank + 1)/2
linear term for quadratic optimization
provide an optional initialState for memory optimization
converged solution
minimize API for cases where gram matrix is provided by the user.
minimize API for cases where gram matrix is provided by the user. If a initialState is not provided by default it constructs it through initialize
symmetric gram matrix of size rank x rank
linear term for quadratic optimization
provide an optional initialState for memory optimization
converged solution
minimize API for cases where gram matrix is updated through updateGram API.
minimize API for cases where gram matrix is updated through updateGram API. If a initialState is not provided by default it constructs it through initialize
linear term for quadratic optimization
provide an optional initialState for memory optimization
converged solution
minimizeAndReturnState API that takes upper triangular entries of the gram matrix specified through primitive array for performance reason and the linear term for quadratic minimization
minimizeAndReturnState API that takes upper triangular entries of the gram matrix specified through primitive array for performance reason and the linear term for quadratic minimization
upper triangular gram matrix specified as primitive array
linear term
provide a initialState using initialState API for memory optimization
converged state from QuadraticMinimizer
minimizeAndReturnState API that takes a symmetric full gram matrix and the linear term for quadratic minimization
minimizeAndReturnState API that takes a symmetric full gram matrix and the linear term for quadratic minimization
gram matrix, symmetric of size rank x rank
linear term
provide a initialState using initialState API for memory optimization
converged state from QuadraticMinimizer
minimizeAndReturnState API gives an advanced control for users who would like to use QuadraticMinimizer in 2 steps, update the gram matrix first using updateGram API and followed by doing the solve by providing a user defined initialState.
minimizeAndReturnState API gives an advanced control for users who would like to use QuadraticMinimizer in 2 steps, update the gram matrix first using updateGram API and followed by doing the solve by providing a user defined initialState. rho is automatically calculated by QuadraticMinimizer from problem structure
linear term for the quadratic optimization
provide a initialState using initialState API
converged state from QuadraticMinimizer
minimizeAndReturnState API gives an advanced control for users who would like to use QuadraticMinimizer in 2 steps, update the gram matrix first using updateGram API and followed by doing the solve by providing a user defined initialState.
minimizeAndReturnState API gives an advanced control for users who would like to use QuadraticMinimizer in 2 steps, update the gram matrix first using updateGram API and followed by doing the solve by providing a user defined initialState. It also exposes rho control to users who would like to experiment with rho parameters of the admm algorithm. Use user-defined rho only if you understand the proximal algorithm well
linear term for the quadratic optimization
rho parameter for ADMM algorithm
provide a initialState using initialState API
use true if you want to hot start based on the provided state
converged state from ADMM algorithm
updateGram API allows user to seed QuadraticMinimizer with upper triangular gram matrix (memory optimization by 50%) specified through primitive arrays.
updateGram API allows user to seed QuadraticMinimizer with upper triangular gram matrix (memory optimization by 50%) specified through primitive arrays. It is exposed for advanced users like Spark ALS where ALS constructs normal equations as primitive arrays
upper triangular gram matrix specified in primitive array
updateGram allows the user to seed QuadraticMinimizer with symmetric gram matrix most useful for cases where the gram matrix does not change but the linear term changes for multiple solves.
updateGram allows the user to seed QuadraticMinimizer with symmetric gram matrix most useful for cases where the gram matrix does not change but the linear term changes for multiple solves. It should be called iteratively from Normal Equations constructed by the user
rank * rank size full gram matrix
Proximal operators and ADMM based Primal-Dual QP Solver
Reference: http://www.stanford.edu/~boyd/papers/admm/quadprog/quadprog.html
It solves problem that has the following structure
1/2 x'Hx + f'x + g(x) s.t Aeqx = b
g(x) represents the following constraints which covers ALS based matrix factorization use-cases
1. x >= 0 2. lb <= x <= ub 3. L1(x) 4. L2(x) 5. Generic regularization on x