Related papers: Scalable Derivative-Free Optimization for Nonlinea…
Zeroth-order (ZO) method has been shown to be a powerful method for solving the optimization problem where explicit expression of the gradients is difficult or infeasible to obtain. Recently, due to the practical value of the constrained…
Many computer vision problems are formulated as the optimization of a cost function. This approach faces two main challenges: (i) designing a cost function with a local optimum at an acceptable solution, and (ii) developing an efficient…
A general framework for solving nonlinear least squares problems without the employment of derivatives is proposed in the present paper together with a new general global convergence theory. With the aim to cope with the case in which the…
This paper studies an unsupervised deep learning-based numerical approach for solving partial differential equations (PDEs). The approach makes use of the deep neural network to approximate solutions of PDEs through the compositional…
Nowadays, Non-Linear Least-Squares embodies the foundation of many Robotics and Computer Vision systems. The research community deeply investigated this topic in the last years, and this resulted in the development of several open-source…
We consider decentralized gradient-free optimization of minimizing Lipschitz continuous functions that satisfy neither smoothness nor convexity assumption. We propose two novel gradient-free algorithms, the Decentralized Gradient-Free…
In this paper, we consider mixed-integer nonsmooth constrained optimization problems whose objective/constraint functions are available only as the output of a black-box zeroth-order oracle (i.e., an oracle that does not provide derivative…
To reduce complexity and achieve scalable performance in high-dimensional black-box settings, we propose a distributed method for nonconvex derivative-free optimization of continuous variables with an additively separable objective, subject…
We consider the problem of unconstrained minimization of a smooth objective function in $\R^n$ in a setting where only function evaluations are possible. While importance sampling is one of the most popular techniques used by machine…
We introduce a novel framework for decentralized projection-free optimization, extending projection-free methods to a broader class of upper-linearizable functions. Our approach leverages decentralized optimization techniques with the…
A tremendous range of design tasks in materials, physics, and biology can be formulated as finding the optimum of an objective function depending on many parameters without knowing its closed-form expression or the derivative. Traditional…
In this experience report, we apply deep active learning to the field of design optimization to reduce the number of computationally expensive numerical simulations. We are interested in optimizing the design of structural components, where…
We study a class of zeroth-order distributed optimization problems, where each agent can control a partial vector and observe a local cost that depends on the joint vector of all agents, and the agents can communicate with each other with…
In this work, we consider methods for solving large-scale optimization problems with a possibly nonsmooth objective function. The key idea is to first specify a class of optimization algorithms using a generic iterative scheme involving…
We consider $\min\{f(x):g(x) \le 0, ~x\in X\},$ where $X$ is a compact convex subset of $\RR^m$, and $f$ and $g$ are continuous convex functions defined on an open neighbourhood of $X$. We work in the setting of derivative-free…
We consider solving nonlinear optimization problems with a stochastic objective and deterministic equality constraints, assuming that only zero-order information is available for both the objective and constraints, and that the objective is…
We develop a mesh-free, derivative-free, matrix-free, and highly parallel localized stochastic method for high-dimensional semilinear parabolic PDEs. The efficiency of the proposed method is built upon four essential components: (i) a…
We propose a new technique for obtaining reduced order models for nonlinear dynamical systems. Specifically, we advocate the use of the recently developed Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the…
Aerodynamic design optimization is an important problem in aircraft design that depends on the interplay between a numerical optimizer and a high-fidelity flow physics solver. Derivative-based, first and (quasi) second order, optimization…
We present a flexible trust region descend algorithm for unconstrained and convexly constrained multiobjective optimization problems. It is targeted at heterogeneous and expensive problems, i.e., problems that have at least one objective…