Convex Integer Quadratic Programming Binary Optimizer
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Solution Overview
Problem
Current quantum annealing systems are limited in translating optimization problems, particularly in solving convex integer quadratic programming issues, as they are mainly suited for binary quadratic programming problems, making it cumbersome to handle a broader range of optimization tasks effectively.
Innovation Solution
A method is developed to convert convex integer quadratic programming problems into constrained and unconstrained binary quadratic programming problems, which can be solved using a binary optimizer by modifying the objective function to include equality constraints as penalty terms and identifying fundamental cubes within a polytope to determine corresponding binary programming problems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If quantum annealing is used to solve optimization problems, then binary quadratic programming problems can be solved, but the translation of general convex integer quadratic programming problems into binary quadratic programming problems is cumbersome and limited
Solution Approach 1:
The patent segments the convex integer quadratic programming problem into multiple binary quadratic programming problems by dividing the feasible region into fundamental cubes. Each fundamental cube corresponds to a binary programming problem that can be solved independently using quantum annealing, thereby enabling the solution of general convex integer quadratic programming problems through a systematic decomposition approach
Solution Approach 2:
The patent introduces an intermediary transformation process that converts the general convex integer quadratic programming problem into a set of binary quadratic programming problems. This intermediary step involves representing the problem using fundamental cubes and their corresponding binary programming formulations, which serve as a bridge between the general problem and the quantum annealing-capable binary problems
2Ease of manufacture
If equality constraints are added to the quadratic objective function as penalty terms, then the problem can be converted into binary quadratic programming format, but the objective function becomes more complex
Solution Approach 1:
The patent converts the complexity introduced by adding penalty terms for equality constraints into a beneficial transformation. By incorporating these penalty terms, the problem is successfully transformed into binary quadratic programming format, which enables solution using quantum annealing. The apparent increase in complexity is justified by the gain in solvability and the systematic approach provided by the fundamental cube decomposition
Data Source
AI summary
A method and system are disclosed for solving a convex integer quadratic programming problem using a binary optimizer, the method comprising use of a processor for receiving a convex integer quadratic programming problem; converting the convex integer quadratic programming problem into a plurality of constrained and unconstrained binary quadratic programming problems and providing the plurality of unconstrained binary quadratic programming problems to the binary optimizer to thereby solve the convex integer quadratic programming problem.