Related papers: Uniform non-convex optimisation via Extremum Seeki…
We generalize the Safe Extremum Seeking algorithm to address the minimization of an unknown objective function subject to multiple unknown inequality and equality constraints, relying on recent results of gradient flow systems. These…
Extremum seeking control (ESC) are optimization algorithms in continuous time, with model-based ESCs using true derivative information of the cost function and model-free ESCs utilizing perturbation-based estimates instead. Stability…
In this paper the finite-time stabilization problem is solved for a linear time-varying system with unknown control direction by exploiting a modified version of the classical extremum seeking algorithm. We propose to use a suitable…
The necessity to find the global optimum of multiextremal functions arises in many applied problems where finding local solutions is insufficient. One of the desirable properties of global optimization methods is \emph{strong homogeneity}…
This paper deals with two kinds of the one-dimensional global optimization problems over a closed finite interval: (i) the objective function $f(x)$ satisfies the Lipschitz condition with a constant $L$; (ii) the first derivative of $f(x)$…
This paper proposes a multivariable extremum seeking scheme using Fast Fourier Transform (FFT) for a network of subsystems working towards optimizing the sum of their local objectives, where the overall objective is the only available…
Convergence of Extremum Seeking (ES) algorithms has been established in the limit of small gains. Using averaging theory and contraction analysis, we propose a framework for computing explicit bounds on the departure of the ES scheme from…
We consider a unique continuation problem where the Dirichlet trace of the solution is known to have finite dimension. We prove Lipschitz stability of the unique continuation problem and design a finite element method that exploits the…
This paper focuses on the further development of the Lie bracket approximation approach for extremum seeking systems. Classical results in this area provide extremum seeking algorithms with exponential convergence rates for quadratic-like…
The paper deals with the extremum seeking problem for a class of cost functions depending only on a part of state variables of a control system. This problem is related to the concept of partial asymptotic stability and analyzed by…
This paper considers the distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of local cost functions by using local information exchange. We first consider a distributed first-order primal-dual…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
Global minimization is a fundamental challenge in optimization, especially in machine learning, where finding the global minimum of a function directly impacts model performance and convergence. This article introduces a novel optimization…
We analyze stability and robustness properties of an extremum seeking scheme that employs oscillatory dither signals with sufficiently large amplitudes and frequencies. Our study takes both input and output disturbances into account. We…
Extremum seeking feedback is a powerful method to steer a dynamical system to an extremum of a partially or completely unknown map. It often requires advanced system-theoretic tools to understand the qualitative behavior of extremum seeking…
In this paper, we propose a distributed first-order algorithm with backtracking linesearch for solving multi-agent minimisation problems, where each agent handles a local objective involving nonsmooth and smooth components. Unlike existing…
We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients.…
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…
The (global) Lipschitz smoothness condition is crucial in establishing the convergence theory for most optimization methods. Unfortunately, most machine learning and signal processing problems are not Lipschitz smooth. This motivates us to…
The aim of this paper is to prove the exponential convergence, local and global, of Adam algorithm under precise conditions on the parameters, when the objective function lacks differentiability. More precisely, we require Lipschitz…