Active Constraint Set Management for Convex Quadratic Programming
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Solution Overview
Problem
Conventional computing devices face challenges in finding the optimal solution for convex quadratic programming problems when multiple inequality constraints are not in a linearly independent relation, leading to decreased computation load and inability to determine the optimal solution.
Innovation Solution
A computing device and method that generate an active constraint set based on an inequality constraint set and initial solution, using a processor with a generation unit, search unit, and updating unit to find and update the active constraint set, determining linear dependence and adding constraints to maintain linear independence, thereby avoiding large computation loads.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the computing device computes the rank of a matrix in each inequality constraint to confirm linear independence, then the reliability of finding the optimal solution is improved, but the computation load becomes large
Solution Approach 1:
The patent performs preliminary action by checking linear independence of inequality constraints before incorporating them into the active constraint set. The linear independence check is performed on constraints that are candidates for addition, ensuring that only linearly independent constraints are added to the active set. This preliminary filtering prevents the computation of matrix rank for all constraints, thereby reducing overall computation load while maintaining reliability in finding the optimal solution.
2Device complexity
If the dimensions of the simultaneous linear equation are decreased due to linearly dependent constraints, then the device complexity is reduced, but the optimal solution cannot be found
Solution Approach 1:
The patent applies preliminary action by performing a linear independence check on inequality constraints before they are added to the active constraint set. The checking unit determines whether each candidate constraint is linearly independent of the existing active constraints. Only constraints that pass this preliminary check are incorporated into the active set, ensuring that the simultaneous linear equations maintain appropriate dimensions and can reliably find the optimal solution while keeping device complexity manageable.
Solution Approach 2:
The patent introduces an intermediary mechanism - the checking unit - that acts as a mediator between the inequality constraints and the active constraint set. This intermediary performs linear independence verification and filters constraints accordingly, preventing linearly dependent constraints from reducing the dimensions of simultaneous linear equations. This intermediary layer ensures that the optimal solution can be found reliably without unnecessarily increasing device complexity.
Data Source
AI summary
A processor of a computing device comprises: a generation unit to generate an active constraint set based on an inequality constraint set and an initial solution; a search unit to find a solution of a simultaneous linear equation generated based on the active constraint set and an evaluation function; and an updating unit to update the active constraint set based on the solution obtained by the search unit. The generation unit adds, to the active constraint set, the first inequality constraint determined as being not linearly dependent on one or more second inequality constraints included in the active constraint set.