NLP Solutions as Asymptotic Values of ODE Trajectories
For researchers in optimization, this offers a potential alternative method, but the lack of empirical validation and comparison to existing methods makes it incremental.
The paper shows that solutions to differentiable constrained optimization problems can be obtained as asymptotic solutions of a single ODE, eliminating the need for solving a sequence of optimization problems. The approach is illustrated on combinatoric optimization and fast analog circuit computation, but no concrete performance numbers are provided.
In this paper, it is shown that the solutions of general differentiable constrained optimization problems can be viewed as asymptotic solutions to sets of Ordinary Differential Equations (ODEs). The construction of the ODE associated to the optimization problem is based on an exact penalty formulation in which the weighting parameter dynamics is coordinated with that of the decision variable so that there is no need to solve a sequence of optimization problems, instead, a single ODE has to be solved using available efficient methods. Examples are given in order to illustrate the results. This includes a novel systematic approach to solve combinatoric optimization problems as well as fast computation of a class of optimization problems using analogic circuits leading to fast, parallel and highly scalable solutions.