Sas Institute Inc.

Riadh Omheni

Joshua David Griffin

Yan Xu

Seyedalireza Yektamaram

Wenwen Zhou

A system and method include dividing training data into training data blocks, determining a support vector subset, distributing the training data blocks and the support vector subset to worker machines, receiving a first set of sub-results from worker machines, combining the first set of sub-results, solving a linear system, distributing a first set of variables to worker machines, receiving a second set of sub-results from worker machines, selecting a step size value and sending the selected step size value to worker machines, receiving updated values of the first set of variables and second set of variables from worker machines, receiving a maximum residual error value from worker machines, selecting a maximum value of the maximum residual error values, responsive to determining that selected maximum value satisfies an optimality condition, outputting a weight value and a bias value, and predicting a label using the weight value and the bias value.

Distributed nonlinear support vector machines

A computer determines a solution to a nonlinear optimization problem. A conjugate gradient (CG) iteration is performed with a first order derivative vector and a second order derivative matrix to update a CG residual vector, an H-conjugate vector, and a residual weight vector. A CG solution vector is updated using a previous CG solution vector, the H-conjugate vector, and the residual weight vector. An eigenvector of the second order derivative matrix having a smallest eigenvalue is computed. A basis matrix is defined that includes a cubic regularization (CR) solution vector, a CR residual vector, the CG solution vector, the CG residual vector, and the eigenvector. A CR iteration is performed to update the CR solution vector. The CR residual vector is updated using the first order derivative vector, the second order derivative matrix, and the updated CR solution vector. The process is repeated until a stop criterion is satisfied.

Cubic regularization optimizer

A computer solves a nonlinear optimization problem. An optimality check is performed for a current solution to an objective function that is a nonlinear equation with constraint functions on decision variables. When the performed optimality check indicates that the current solution is not an optimal solution, a barrier parameter value is updated, and a Lagrange multiplier value is updated for each constraint function based on a result of a complementarity slackness test. The current solution to the objective function is updated using a search direction vector determined by solving a primal-dual linear system that includes a dual variable for each constraint function and a step length value determined for each decision variable and for each dual variable. The operations are repeated until the optimality check indicates that the current solution is the optimal solution or a predefined number of iterations has been performed.

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Riadh Omheni