Data Mapping

The solution to many industrial problems can be understood through the lens of optimization: proper optimization techniques provide a solution in terms of inputs into a process to help businesses or researchers make resource allocation decisions. With applications across a broad set of problems, ranging from manufacturing to airline plane allocation decisions, optimization techniques have helped companies improve outcomes across nearly every sector:

Optimal Control Models
As the basis for variational calculus optimization, optimal control emerged from engineering and found a variety of applications in economic planning. In particular, the system defines a series of differential equations that model the path of costs according to changes in variables. By starting from an initial condition (state), the model seeks to understand how to maximize a function limited by a series of constraints – for example, engineers may want to evaluate the best possible fuel economy of a given design based upon road conditions and optimal control can help suggest improvements in controls to help improve these outcomes. In general, problems in the field are non-linear and often solved by way of numerical methods, which require computing solutions such as MATLAB to find a numerical solution.

Convex Optimization
As the basis for optimization on classical economic problems, convex optimization seeks to answer the question of finding the maximum or minimum values within a function. As a result, a variety of problems, from theoretical utility maximization to least-squares regression analysis, rely upon convex techniques to find solutions. A common problem within the field is to minimize a function (such as costs) subject to constraints (such as output requirements or labor costs) to determine optimal business allocation, especially when managers are allocating resources across various locations.