LCvx Concept

Topics: Convex Optimization

Lossless Convexification (LCvx) is a mathematical technique used to transform a nonconvex optimization problem into an equivalent convex problem. It does so by relaxing the nonconvex constraint into a convex set and then using Pontryagin's maximum principle to show that the solution of the relaxed problem is the globally optimal solution to the original problem.

In short, it consists of 2 stages:

• finding a convex lifting of the feasible nonconvex input set
• showing that the optimal solution of the lifted problem projects back to a feasible and optimal solution of the original problem

The following image shows a summary of the different optimization problems for which LCvx was applied.

References

1. Convex Optimization for Trajectory Generation - A Tutorial on Generating Dynamically Feasible Trajectories Reliably and Efficiently