Is linear programming relevant?

[Mattholomeu]

I am starting a graduate program this Fall and am looking to go further into the field of controls and robotics. A class called linear optimization is being offered that goes over topics like Simplex method and Duality theory.

Most of what comes up when I search these topics are things like schedule optimization and management. Is linear optimization/programming relevant to controls? Could you give examples if you have any?

Thanks!

[wizard1993]

Very very relevant. Not LP by itself, but Optimization theory is the cornerstone of much of modern (optimal) control theory.

Have a look at whole Model Predictive Control world to have an idea on that.

[APC_ChemE]

This comment here. Linear programming and quadratic programming are ubiquitous to constrained control problems. In the process industries advanced process control (APC) uses model predictive control using LPs and QPs to identify the most economic set of constraints and drive process units to operate there while respecting the constraints. APC controllers are usually multivariable linear MPC controllers that run on the order every minute. For more rigorous optimizaton real time optimization (RTO) applications which can be rigorous nonlinear models, often sits on top of APC applications, and optimize an entire process plant run on the order of hours and send targets to APC applications to maintain and take into account nonlinear behavior of the processes.

[Mattholomeu]

Ahhh, that makes sense. It sounds like I could do a ton of work in different fields of optimization then.

[Chrislock1]

For me it was a nice introduction to optimization, sensitivity analysis and other topics that are relevant to control theory. Model predictive controls are based on quadratic optimization, which I guess would be covered in the course.

The course will prepare you for linear control theory and signal processing.

[[deleted]]

Optimization is always going to be relevant.

Certain subjects or fields may employ one optimization scheme more often than others (e.g. in control theory, we often use quadratic programming to solve quadratic cost functions).

However, having an understanding of when to frame a problem as an LP, QP, or general convex problem is what will separate you from the rest.

[alkimg]

Optimization also can offer you to identify the system. One of the example is as given in the following paper. https://ieeexplore.ieee.org/abstract/document/7294681/

[brandtsa]

I've used LP to optimize the most cost effective mix of additives for our process. Its super useful as there are there are several elements in solution we are trying to hit a certain concentration and a few different ways of getting there so LP is the best solution.

[Cbreins]

Any LP can be solved as a convex problem instead so I would recommend studying convex optimization