Path integral formulation of Brownian trajectories is employed to re-derive the steepest descent path (SDP). An analogy between the mechanics of overdamped tra-jectories and a Hamiltonian system is found and exploited. The SDP is a special path selected from the curves that connect two predetermined xed conngurations. One xed connguration is the reactant and the second is the product. It is the...

The negative gradient direction to find local minimizers has been associated with the classical steepest descent method which behaves poorly except for very well conditioned problems. We stress out that the poor behavior of the steepest descent methods is due to the optimal Cauchy choice of steplength and not to the choice of the search direction. We discuss over and under relaxation of the opt...

We consider n non-intersecting Brownian motion paths with p prescribed starting positions at time t = 0 and q prescribed ending positions at time t = 1. The positions of the paths at any intermediate time are a determinantal point process, which in the case p = 1 is equivalent to the eigenvalue distribution of a random matrix from the Gaussian unitary ensemble with external source. For general ...

This paper presents a new method for accelerating intensity-modulated radiation therapy (IMRT) optimization using voxel sampling. Rather than calculating the dose to the entire patient at each step in the optimization, the dose is only calculated for some randomly selected voxels. Those voxels are then used to calculate estimates of the objective and gradient which are used in a randomized vers...

Despite the reported effectiveness of analytical algorithms in facility layout planning, a detailed literature survey suggests a lack of new analytical methods in recent years. This paper focuses on open space facilities layout planning that involves modules with constant aspect ratios. We propose a construction-cum-improvement algorithm involving a novel combination of a boundary search-based ...

Given data points p0, . . . , pN on a Riemannian manifold M and time instants 0 = t0 < t1 < . . . < tN = 1, we consider the problem of finding the curve γ on M that best approximates the data points at the given instants. In this work, γ is expressed as the curve that minimizes the weighted sum of a least-squares term penalizing the lack of fitting to the data points and a regularity term defin...

A general framework is proposed for the study of real-time algorithms. The framework uniies previous algorithmic deenitions of real-time computation. In it, state space traversal is used as a model for computational problems in a real-time environment. The proposed framework also employs a paradigm, known as discrete steepest descent, for algorithms designed to solve these problems. Sequential ...

An efficient method for finding a better maximizer of computationally extensive probability distributions is proposed on the basis of a Bayesian optimization technique. A key idea of the proposed method is to use extreme values of acquisition functions by Gaussian processes for the next training phase, which should be located near a local maximum or a global maximum of the probability distribut...

Standard backpropagation and many procedures derived from it use the steepest-descent method to minimize a cost function. In this paper, we present a new genetic algorithm, dynamic self-adaptation, to accelerate steepest descent as it is used in iterative procedures. The underlying idea is to take the learning rate of the previous step, to increase and decrease it slightly, to evaluate the cost...

The purpose of this study is to show some mathematical aspects of the adjoint method that is a numerical method for the Cauchy problem, an inverse boundary value problem. The adjoint method is an iterative method based on the variational formulation, and the steepest descent method minimizes an objective functional derived from our original problem. The conventional adjoint method is time-consu...