Optimized batched polytope projection

1 . A method for calculation of an estimated solution which satisfies a constraint polytope, the method including:

initializing, at a polytope controller on a high-throughput scalable parallel graphics processor, the constraint polytope;

receiving, at the polytope controller on the high-throughput scalable parallel graphics processor, a first point batch from an external computer system, the first point batch including a plurality of data points representing a plurality of transactions;

performing, at the polytope controller on the high-throughput scalable parallel graphics processor, a uniform batch projection, the uniform batch projection resulting in a failure to project at least a corresponding one of the plurality of data points to the constraint polytope that would have been successfully projected to the constraint polytope using a corresponding individual optimal projection for the corresponding one of the plurality of data points thereby achieving higher calculation throughput at a cost of lower calculation accuracy;

determining, at the polytope controller on the high-throughput scalable parallel graphics processor, whether the projection satisfies the constraint polytope within a defined tolerance;

generating, at the polytope controller on the high-throughput scalable parallel graphics processor, a dynamic adjustment for use with a second point batch for the constraint polytope that causes the second point batch to satisfy the constraint polytope at least within the defined tolerance, the dynamic adjustment accounting for a composition change between the first point batch and the second point batch; and

reducing, consistent with the dynamic adjustment, a margin requirement for the plurality of transactions.

2 . The method of claim 1 , wherein initializing the constraint polytope includes:

generating at least one internal structure for the constraint polytope.

3 . The method of claim 2 , wherein the at least one internal structure includes a linear inequality.

4 . The method of claim 1 , wherein initializing the constraint polytope includes:

defining default values for an adaptive mechanism.

5 . The method of claim 1 , wherein initializing the constraint polytope includes:

determining an acceptable fail rate for a proportion of the plurality of data points projected within the constraint polytope.

6 . The method of claim 1 , wherein initializing the constraint polytope includes:

determining a feasibility tolerance for a quantity of the plurality of data points that exceeds an inequality of the constraint polytope.

7 . The method of claim 1 , further including:

receiving the second point batch including a second plurality of data points;

analyzing the second plurality of data points;

performing a second uniform batch projection of the second plurality of data points to the constraint polytope;

determining whether the second uniform batch projection satisfies the constraint polytope; and

generating a second dynamic adjustment for use with a third point batch for the constraint polytope.

8 . The method of claim 1 , wherein a time complexity for the uniform batch projection approximates O (n).

9 . The method of claim 1 , wherein a time complexity for the uniform batch projection is less than a time complexity for a quadratic optimization projection to the constraint polytope.

10 . The method of claim 1 , wherein a time complexity for the initialization of the constraint polytope is O(mn 2 ) or O(n 3 ).

11 . The method of claim 1 , further including:

determining an optimal set of values for the first point batch based on the dynamic adjustment.

12 . The method of claim 1 , wherein a time complexity of the uniform batch projection is proportionate to a number of inequalities of the constraint polytope after initialization.

13 . A system for calculation of an estimated solution which satisfies a constraint polytope, the system including:

a memory;

a processor including at least a high-throughput scalable parallel graphics processing unit;

the memory including first logic configured to cause the processor to initialize, via a polytope controller on the high-throughput scalable parallel graphics processing unit, the constraint polytope;

the memory including second logic configured to cause the processor to receive, at the polytope controller, a first point batch from an external computer system, the first point batch including a plurality of data points representing a plurality of transactions;

the memory including third logic configured to cause the processor to perform, at the polytope controller, a uniform batch projection, the uniform batch projection resulting in a failure to project at least a corresponding one of the plurality of data points to the constraint polytope that would have been successfully projected to the constraint polytope using a corresponding individual optimal projection for the corresponding one of the plurality of data points thereby achieving higher calculation throughput at a cost of lower calculation accuracy;

the memory including fourth logic configured to cause the processor to determine, at the polytope controller on a high-throughput scalable parallel graphics processor, whether the projection satisfies the constraint polytope within a defined tolerance;

the memory including fifth logic configured to cause the processor to generate, at the polytope controller, a dynamic adjustment for use with a second point batch for the constraint polytope, wherein the dynamic adjustment causes the second point batch to satisfy the constraint polytope at least within the defined tolerance, the dynamic adjustment accounting for a composition change between the first point batch and the second point batch; and

the memory including sixth logic configured to cause the processor to reduce, at the polytope controller and consistent with the dynamic adjustment, a margin requirement for the plurality of transactions.

14 . The system of claim 13 , further including:

a user input device configured to receive at least one user selection for the defined tolerance.

15 . The system of claim 13 , wherein the defined tolerance includes a failure rate threshold that defines a limit for a proportion of the plurality of data points projected within the constraint polytope.

16 . The system of claim 13 , wherein the defined tolerance includes a feasibility tolerance that defines a limit for a quantity of the plurality of data points that exceeds an inequality of the constraint polytope.

17 . The system of claim 13 , further including:

a display configured to present data indicative of the uniform batch projection.

18 . A non-transitory machine-readable medium including instructions that when executed are configured to cause a processor to:

initialize, at a polytope controller on a high-throughput scalable parallel graphics processor, a constraint polytope;

receive, at the polytope controller on the high-throughput scalable parallel graphics processor, a first point batch from an external computer system, the first point batch including a plurality of data points representing transactions;

perform, at the polytope controller on the high-throughput scalable parallel graphics processor, a uniform batch projection, the uniform batch projection resulting in a failure to project at least a corresponding one of the plurality of data points to the constraint polytope that would have been successfully projected to the constraint polytope using a corresponding individual optimal projection for the corresponding one of the plurality of data points thereby achieving higher calculation throughput at a cost of lower calculation accuracy;

determine, at the polytope controller on the high-throughput scalable parallel graphics processor, whether the uniform batch projection satisfies the constraint polytope within a defined tolerance;

generate, at the polytope controller on the high-throughput scalable parallel graphics processor, a dynamic adjustment for use with a second point batch for the constraint polytope, wherein the dynamic adjustment causes the second point batch to satisfy the constraint polytope at least within the defined tolerance, the dynamic adjustment accounting for a composition change between the first point batch and the second point batch; and

reduce, at the polytope controller and consistent with the dynamic adjustment, a margin requirement for the plurality of transactions.

19 . The non-transitory machine-readable medium of claim 18 , wherein a time complexity for the uniform batch projection approximates O(n).

20 . The non-transitory machine-readable medium of claim 18 , wherein a time complexity for the uniform batch projection is less than a time complexity for a quadratic optimization projection to the constraint polytope.