Related papers: Topology trivialization and large deviations for t…
We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…
We give an asymptotic evaluation of the complexity of spherical p-spin spin-glass models via random matrix theory. This study enables us to obtain detailed information about the bottom of the energy landscape, including the absolute minimum…
In this paper we consider the unconstrained minimization problem of a smooth function in ${\mathbb{R}}^n$ in a setting where only function evaluations are possible. We design a novel randomized derivative-free algorithm --- the stochastic…
The topological derivative represents the sensitivity of a domain-dependent functional with respect to a local perturbation of the domain and is a valuable tool in topology optimization. Motivated by an application from electrical…
In this work, we investigate stochastic quasi-Newton methods for minimizing a finite sum of cost functions over a decentralized network. In Part I, we develop a general algorithmic framework that incorporates stochastic quasi-Newton…
The design of minimum-compliance bending-resistant structures with continuous cross-section parameters is a challenging task because of its inherent non-convexity. Our contribution develops a strategy that facilitates computing all…
We investigate the properties of local minima of the energy landscape of a continuous non-convex optimization problem, the spherical perceptron with piecewise linear cost function and show that they are critical, marginally stable and…
A trivializing map is a field transformation whose Jacobian determinant exactly cancels the interaction terms in the action, providing a representation of the theory in terms of a deterministic transformation of a distribution from which…
The random cost problem is the problem of finding the minimum in an exponentially long list of random numbers. By definition, this problem cannot be solved faster than by exhaustive search. It is shown that a classical NP-hard optimization…
The reduced-rank method exploits the distortion-variance tradeoff to yield superior solutions for classic problems in statistical signal processing such as parameter estimation and filtering. The central idea is to reduce the variance of…
The use of topology optimization methods for the design of electric machines has become increasingly popular over the past years. Due to a desired increase in power density and a recent trend to high speed machines, thermal aspects play a…
In this paper, we study the form over the minimum spanning tree problem (MST) from which we will derive an intuitively generalized model and new methods with the upper bound of runtimes of logarithm. The new pattern we made has taken…
In this paper, we perform a rigourous version of shape and topological derivatives for optimizations problems under constraint Helmoltz problems. A shape and topological optimization problem is formulated by introducing cost functional. We…
Distributing points on a (possibly high-dimensional) sphere with minimal energy is a long-standing problem in and outside the field of mathematics. This paper considers a novel energy function that arises naturally from statistics and…
A novel approach for the solution of the wind farm layout optimization problem is presented. The annual energy production is maximized with constraints on the minimum and maximum number of wind turbines placed, and on the minimum spacing…
Marginal optima are minima or maxima of a function with many nearly flat directions. In settings with many competing optima, marginal ones tend to attract algorithms and physical dynamics. Often, the important family of marginal attractors…
We present a numerical method to efficiently solve optimization problems governed by large-scale nonlinear systems of equations, including discretized partial differential equations, using projection-based reduced-order models accelerated…
We study the least squares regression problem \begin{align*} \min_{\Theta \in \mathcal{S}_{\odot D,R}} \|A\Theta-b\|_2, \end{align*} where $\mathcal{S}_{\odot D,R}$ is the set of $\Theta$ for which $\Theta = \sum_{r=1}^{R} \theta_1^{(r)}…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
Determination of the classical ground state arrangement of $N$ charges on the surface of a sphere (Thomson's problem) is a challenging numerical task. For special values of $N$ we have obtained using the ring removal method of Toomre, low…