Problems, such as finding optimal reaction paths, require minimizing an integral involving an exponential of a function. Conventional minimization methods are not well suited to such problems because they hasten convergence by assuming locally quadratic behavior of the objective. However, if the problem is expressed as a dynamical system performing gradient descent, it is possible to do scaling to remove exponential factors, which permits the use of solution methods based on a local linear model. For the case of computing a curve rather than a function, there is another difficulty, namely, arbitrariness in its parameterization. This requires the imposition of a constraint, which is difficult to formulate in a stable way. Moreover, an appropriate constraint reintroduces exponential factors, causing difficulties due to the limited exponent range of floating-point numbers.
This is joint work with R. Zhao, H. Huang, M. Wolff, and C. Post.
