A method and device determines an optimization solution for an optimization problem. The method includes receiving the optimization problem having cost functions and variables in which each of the cost functions has a predetermined relationship with select ones of the variables. The variables comprise a sub-solution of a spline indicative of a curved path along an estimated trajectory. The method includes generating a first message for each of the cost functions for each corresponding variable based upon the relationship and a second message for each of the variables for each corresponding cost function based upon the relationship. The method includes generating a disagreement variable for each corresponding pair of variables and cost functions measuring a disagreement value between the first and second beliefs. The method includes forming a consensus between the first and second messages until the optimization solution is determined.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method, comprising: (a) receiving an optimization problem, the optimization problem including a plurality of cost functions and a plurality of variables, the cost functions representing possible costs for values of the variables in the optimization problem, each of the cost functions having a predetermined relationship with select ones of the variables, wherein the variables comprise at least one sub-solution to at least one sub-problem associated with the optimization problem, the sub-solution being a spline indicative of a curved path along an estimated trajectory; (b) generating a first message for each of the cost functions for each corresponding variable based upon the respective predetermined relationship, the first message indicating a first belief that the corresponding variable has a first value when the optimization problem is solved, the first message having a respective first weight indicating a certainty of the first message; (c) generating a second message for each of the variables for each corresponding cost function based upon the respective predetermined relationship, the second message indicating a second belief that the corresponding variable has a second value when the optimization problem is solved, the second message having a respective second weight indicating a certainty of the second message; (d) generating a disagreement variable for each corresponding pair of variables and cost functions measuring a disagreement value between the first and second beliefs; (e) repeating steps (b), (c), and (d) until a consensus is formed between the first and second messages, a subsequent first message being modified based upon the second message, its corresponding second weight, and the corresponding disagreement variable, and a subsequent second message being modified based upon the first message, its corresponding first weight, and the corresponding disagreement variable; and (f) determining an optimization solution based upon the consensus. 2. The method of claim 1, wherein the optimization problem is a multi-agent trajectory planning problem including a plurality of agents moving from an initial position. 3. The method of claim 2, wherein the multi-agent trajectory planning problem further includes a predetermined end position. 4. The method of claim 2, wherein the at least one sub-problem is associated with factors considered in the optimization problem. 5. The method of claim 4, wherein the factors comprise a collision avoidance, a soft objective, a continuous first derivative, a line obstacle, a maximum velocity, a maximum velocity, a maximum acceleration, a maximum angular velocity, or a combination thereof. 6. The method of claim 5, wherein select ones of the factors are solved using Sequential Least Squares Quadratic Programming (SLSQP). 7. The method of claim 2, wherein each agent has a respective effective radius, the effective radius incorporating a physical dimension of the agent and a predetermined error margin. 8. The method of claim 2, wherein the agents move based upon one of an automation or a user received instruction, the user received instruction being modified based upon the optimization solution. 9. The method of claim 1, wherein each of the first and second weights is one of a zero weight, an infinite weight, and a standard weight. 10. The method of claim 3, wherein the multi-agent trajectory planning problem is the plurality of agents moving from the initial position on a circle to an antipodal position on the circle. 11. A device, comprising: a processor coupled to a memory, wherein the processor is programmed to determine an optimization solution to an optimization problem by: (a) receiving the optimization problem, the optimization problem including a plurality of cost functions and a plurality of variables, the cost functions representing possible costs for values of the variables in the optimization problem, each of the cost functions having a predetermined relationship with select ones of the variables, wherein the variables comprise at least one sub-solution to at least one sub-problem associated with the optimization problem, the sub-solution being a spline indicative of a curved path along an estimated trajectory; (b) generating a first message for each of the cost functions for each corresponding variable based upon the respective predetermined relationship, the first message indicating a first belief that the corresponding variable has a first value when the optimization problem is solved, the first message having a respective first weight indicating a certainty of the first message; (c) generating a second message for each of the variables for each corresponding cost function based upon the respective predetermined relationship, the second message indicating a second belief that the corresponding variable has a second value when the optimization problem is solved, the second message having a respective second weight indicating a certainty of the second message; (d) generating a disagreement variable for each corresponding pair of variables and cost functions measuring a disagreement value between the first and second beliefs; (e) repeating steps (b), (c), and (d) until a consensus is formed between the first and second messages, a subsequent first message being modified based upon the second message, its corresponding second weight, and the corresponding disagreement variable, and a subsequent second message being modified based upon the first message, its corresponding first weight, and the corresponding disagreement variable; and (f) determining the optimization solution based upon the consensus. 12. The device of claim 11, wherein the optimization problem is a multi-agent trajectory planning problem including a plurality of agents moving from an initial position. 13. The device of claim 12, wherein the multi-agent trajectory planning problem further includes a predetermined end position. 14. The device of claim 12, wherein the at least one sub-problem is associated with factors considered in the optimization problem. 15. The device of claim 14, wherein the factors comprise a collision avoidance, a soft objective, a continuous first derivative, a line obstacle, a maximum velocity, a maximum velocity, a maximum acceleration, a maximum angular velocity, or a combination thereof. 16. The device of claim 15, wherein select ones of the factors are solved using Sequential Least Squares Quadratic Programming (SLSQP). 17. The device of claim 12, wherein each agent has a respective effective radius, the effective radius incorporating a physical dimension of the agent and a predetermined error margin. 18. The device of claim 12, wherein the agents move based upon one of an automation or a user received instruction, the user received instruction being modified based upon the optimization solution. 19. The device of claim 11, wherein each of the first and second weights is one of a zero weight, an infinite weight, and a standard weight. 20. A non-transitory computer readable storage medium with an executable program stored thereon, wherein the program instructs a microprocessor to perform operations comprising: (a) receiving an optimization problem, the optimization problem include a plurality of cost functions and a plurality of variables, the cost functions representing possible costs for values of the variables in the optimization problem, each of the cost functions having a predetermined relationship with select ones of the variables, wherein the variables comprise at least one sub-solution to at least one sub-problem associated with the optimization problem, the sub-solution being a spline indicative of a curved path along an estimated trajectory; (b) generating a first message for each of the cost functions for each corresponding variable based upon the respective predetermined relationship, the first message indicating a first belief that the corresponding variables has a first value when the optimization problem is solved, the first message having a respective first weight indicating a certainty of the first message; (c) generating a second message for each of the variables for each corresponding cost function based upon the respective predetermined relationship, the second message indicating a second belief that the corresponding variable has a second value when the optimization is solved, the second message having a respective second weight indicating a certainty of the second message; (d) generating a disagreement variable for each corresponding pair of variables and cost functions measuring a disagreement value between the first and second beliefs; (e) repeating steps (b), (c), and (d) until a consensus is formed between the first and second messages, a subsequent first message being modified based upon the second message, its corresponding second weight, and the corresponding disagreement variable, and a subsequent second message being modified based upon the first message, its corresponding first weight, and the corresponding disagreement variable; and (f) determining an optimization solution based upon the consensus.