This letter addresses distributed optimization, where a network of agents wants to minimize global strongly convex objective function. The function can be written as sum local functions, each which is associated with an agent. We propose continuous-time mirror descent algorithm that uses purely information converge the optimum. Unlike previous work on descent, we incorporate integral feedback i...

We analyze an infinite dimensional, geometrically constrained shape optimization problem for magnetically driven microswimmers (locomotors) in three-dimensional (3-D) Stokes flow and give a well-posed descent scheme for computing optimal shapes. The problem is inspired by recent experimental work in this area. We show the existence of a minimizer of the optimization problem using analytical too...

The paper discusses about the Choquet Fuzzy Integral (CFI) based identification and control of a Real Time Dynamical System. The plant is modeled using Choquet fuzzy Integral based Neural Network with Gradient Descent as learning algorithm. This model is used for designing and simulating CFI based controller. Then this designed controller is implemented on real time system through MATLAB. Final...

The gradient descent is a general method to find a local minimum of a smooth function f(z1, . . . , zd). The method utilizes the observation that f(p) decreases if one goes from a point z = p to a “nice” direction, which is usually −(∇f)(p). As textbooks on optimizations present (see, e.g., [5], [16]), we have a lot of achievements on this method and its variations. We suggest a new variation o...

This paper is an expository survey of the basic theory of regularization for Fredholm integral equations of the first kind and related background material on inverse problems. We begin with an historical introduction to the field of integral equations of the first kind, with special emphasis on model inverse problems that lead to such equations. The basic theory of linear Fredholm equations of ...

The usual way to determine the asymptotic behavior of the Chebyshev coefficients for a function is to apply the method of steepest descent to the integral representation of the coefficients. However, the procedure is usually laborious. We prove an asymptotic upper bound on the Chebyshev coefficients for the kth integral of a function. The tightness of this upper bound is then analyzed for the c...