Constrained Optimization via Alternating Direction Multipliers
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Solution Overview
Problem
Existing methods face challenges in efficiently solving constrained optimization problems, particularly in finding the ground state of interaction models, which are crucial for solving social and physical phenomena, due to limitations in search algorithms for constrained mixed-binary quadratic programming.
Innovation Solution
An information processing system that converts constrained mixed-binary quadratic programming problems into an augmented Lagrange function, using the alternating direction method of multipliers with two separate optimization processes to find optimal solutions for both the objective function and constraint expressions, allowing for parallel updates and efficient search.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional search algorithms are used for constrained mixed-binary quadratic programming, then the method is simple to implement, but the search speed for optimal solutions is slow
Solution Approach 1:
The patent segments the constrained optimization problem into two separate sub-problems: an unconstrained mixed-binary quadratic programming problem (for variable x) and a constrained problem (for variable y). By dividing the original problem into manageable parts that can be solved using different algorithms, the system achieves faster search speeds while maintaining implementation feasibility.
Solution Approach 2:
The patent implements dynamic alternation between two different search algorithms (simulated annealing for unconstrained problems and another algorithm for constrained problems) within the alternating direction method of multipliers framework. This dynamic approach allows the system to adaptively switch between algorithms based on the problem type, improving overall search efficiency.
2Productivity
If a single optimization algorithm is used for both objective function and constraint, then the algorithm is simple, but the optimization efficiency is limited
Solution Approach 1:
The patent applies different optimization algorithms to different parts of the problem: simulated annealing is used for the unconstrained sub-problem while another algorithm is used for the constrained sub-problem. This localized approach allows each algorithm to be optimized for its specific task, improving overall optimization efficiency while maintaining operational clarity.
Solution Approach 2:
The alternating direction method of multipliers serves as an intermediary framework that coordinates between the two different optimization algorithms. It manages the interaction between the unconstrained and constrained sub-problems, enabling efficient optimization without requiring a single complex algorithm to handle both aspects.
Data Source
AI summary
Search for an optimal solution of a constrained optimization problem that includes search for a ground state of an interaction model is sufficiently executed. An information processing system executes a first search process of performing search for an optimal solution of a first variable vector that optimizes an augmented Lagrange function in an alternating direction method of multipliers, using an optimization algorithm of an unconstrained mixed-binary quadratic programming problem, and a second search process of performing search for an optimal solution of a second variable vector that optimizes the augmented Lagrange function in the alternating direction method of multipliers, using another algorithm. The information processing system repeatedly executes the second search process performed using the optimal solution of the first variable vector determined by the first search process and the first search process performed using the optimal solution of the second variable vector determined by the second search process.