Properties of Convex Optimization

Topics: Convex Optimization

Convex optimization refers to a class of optimization problems that seek to minimize a convex objective function while satisfying a set of convex constraints.

In general, convexity is what makes the difference between easy and hard optimization problems. Convex optimization is appealing because of the following properties:

• a globally optimal solution is found if a feasible solution exists
• a certificate of infeasibility is provided when a feasible solution does not exist
• the runtime complexity is polynomial in the problem size
• the algorithms can self-initialize, eliminating the need for an expert initial guess

References

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