公开(公告)号：US11062219B1

公开(公告)日：2021-07-13

申请号：US17106488

申请日：2020-11-30

Applicant: SAS Institute Inc.

Inventor： Joshua David Griffin ,  Riadh Omheni ,  Yan Xu

IPC: G06N5/04 ,  G06N20/00

Abstract: 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.

公开(公告)号：US11983631B1

公开(公告)日：2024-05-14

申请号：US18511092

申请日：2023-11-16

Applicant: SAS Institute Inc.

Inventor： Wenwen Zhou ,  Joshua David Griffin ,  Riadh Omheni ,  Seyedalireza Yektamaram ,  Yan Xu

IPC: G06N3/08 ,  G06F17/16

CPC classification number: G06N3/08 ,  G06F17/16

Abstract: 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.