Optimization methods and systems using proxy constraints

A non-transitory computer readable medium having instructions that, when executed by one or more processors, cause the one or more processors to:

• receive a plurality of input settings from a client device, the plurality of input settings defining an optimization strategy;
• train a machine learning algorithm for determining a relationship between a non-linear constraint and a linear proxy constraint, wherein the relationship includes a misalignment between the non-linear constraint and the linear proxy constraint or a disparity between the non-linear constraint and the linear proxy constraint, wherein the training includes the machine learning algorithm tracking execution results of the relationship;
• modify the linear proxy constraint based on the relationship and the plurality of input settings;
• replace the non-linear constraint within a system of equations with the modified linear proxy constraint;
• determine whether a solution satisfies a convergence criterion using the system of equations based on the plurality of input settings and the linear proxy constraint replacing the non-linear constraint within the system of equations;
• responsive to determining the solution satisfies the convergence criterion, modify a distribution of items based on the optimization strategy;
• and
• responsive to determining the solution does not satisfy the convergence criterion, adjust one or more of the plurality of input settings.

A system comprising:

• one or more processors;
• memory having instructions that, when executed by the one or more processors, cause the one or more processors to:
• receive a plurality of input settings from a client device, the plurality of input settings defining an optimization strategy;
• train a machine learning algorithm for determining a relationship between a non-linear constraint and a linear proxy constraint, wherein the relationship includes a misalignment between the non-linear constraint and the linear proxy constraint or a disparity between the non-linear constraint and the linear proxy constraint, wherein the training includes the machine learning algorithm tracking execution results of the relationship;
• modify the linear proxy constraint based on the relationship and the plurality of input settings;
• replace the non-linear constraint within a system of equations with the modified linear proxy constraint;
• determine whether a solution satisfies a convergence criterion using the system of equations based on the plurality of input settings and the linear proxy constraint replacing the non-linear constraint within the system of equations;
• responsive to determining the solution satisfies the convergence criterion, modify a distribution of items based on the optimization strategy;
• and
• responsive to determining the solution does not satisfy the convergence criterion, adjust one or more of the plurality of input settings.