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
- x >= 0
- lb <= x <= ub
- L1(x)
- L2(x)
- Generic regularization on x
- Value Params
- Aeq
rhs matrix for equality constraints
- abstol
ADMM absolute tolerance
- alpha
over-relaxation parameter default 1.0 1.5 - 1.8 can improve convergence
- beq
lhs constants for equality constraints
- nGram
rank of dense gram matrix
- proximal
proximal operator to be used
- reltol
ADMM relative tolerance
- Companion
- object
Type members
Classlikes
Value members
Concrete methods
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
- Returns
the state for the optimizer
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
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
- Value Params
- initialState
provide an optional initialState for memory optimization
- q
linear term for quadratic optimization
- Returns
converged solution
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
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
- Value Params
- H
symmetric gram matrix of size rank x rank
- initialState
provide an optional initialState for memory optimization
- q
linear term for quadratic optimization
- Returns
converged solution
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
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
- Value Params
- initialState
provide an optional initialState for memory optimization
- q
linear term for quadratic optimization
- upper
upper triangular gram matrix of size rank x (rank + 1)/2
- Returns
converged solution
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
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
- Value Params
- initialState
provide a initialState using initialState API
- q
linear term for the quadratic optimization
- resetState
use true if you want to hot start based on the provided state
- rho
rho parameter for ADMM algorithm
- Returns
converged state from ADMM algorithm
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
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
- Value Params
- initialState
provide a initialState using initialState API
- q
linear term for the quadratic optimization
- Returns
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
- Value Params
- H
gram matrix, symmetric of size rank x rank
- initialState
provide a initialState using initialState API for memory optimization
- q
linear term
- Returns
converged state from QuadraticMinimizer
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
- Value Params
- initialState
provide a initialState using initialState API for memory optimization
- q
linear term
- upper
upper triangular gram matrix specified as primitive array
- Returns
converged state from QuadraticMinimizer
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
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
- Value Params
- H
rank * rank size full gram matrix
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
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
- Value Params
- upper
upper triangular gram matrix specified in primitive array