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In this paper, we consider the decentralized optimization problems with generalized orthogonality constraints, where both the objective function and the constraint exhibit a distributed structure. Such optimization problems, albeit…
Optimization-based controller tuning is challenging because it requires formulating optimization problems explicitly as functions of controller parameters. Safe learning algorithms overcome the challenge by creating surrogate models from…
In this work, multi-variable derivative-free optimization algorithms for unconstrained optimization problems are developed. A novel procedure for approximating the gradient of multi-variable objective functions based on non-commutative maps…
Gradient Descent (GD) and Conjugate Gradient (CG) methods are among the most effective iterative algorithms for solving unconstrained optimization problems, particularly in machine learning and statistical modeling, where they are employed…
We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation…
This paper studies a class of distributed optimization problems with coupled equality constraints in networked systems. Many existing distributed algorithms rely on solving local subproblems via the $\operatorname{argmin}$ operator in each…
For visual tracking, an ideal filter learned by the correlation filter (CF) method should take both discrimination and reliability information. However, existing attempts usually focus on the former one while pay less attention to…
We study the navigation problem for a robot moving amidst static and dynamic obstacles and rely on a hierarchical approach to solve it. First, the reference trajectory is planned by the safe interval path planning algorithm that is capable…
We propose a simple interpolation-based method for the efficient approximation of gradients in neural ODE models. We compare it with the reverse dynamic method (known in the literature as "adjoint method") to train neural ODEs on…
Decarbonization of the transport sector sets increasingly strict demands to maximize thermal efficiency and minimize greenhouse gas emissions of Internal Combustion Engines. This has led to complex engines with a surge in the number of…
The design space of dynamic multibody systems (MBSs), particularly those with flexible components, is considerably large. Consequently, having a means to efficiently explore this space and find the optimum solution within a feasible…
Gradient tracking methods have emerged as one of the most popular approaches for solving decentralized optimization problems over networks. In this setting, each node in the network has a portion of the global objective function, and the…
State-of-the-art methods for data-driven modelling of non-linear dynamical systems typically involve interactions with an expert user. In order to partially automate the process of modelling physical systems from data, many EA-based…
This work studies constrained stochastic optimization problems where the objective and constraint functions are convex and expressed as compositions of stochastic functions. The problem arises in the context of fair classification, fair…
We design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two…
We introduce the notion of heterogeneous calibration that applies a post-hoc model-agnostic transformation to model outputs for improving AUC performance on binary classification tasks. We consider overconfident models, whose performance is…
When an inverse problem is solved by a gradient-based optimization algorithm, the corresponding forward and adjoint problems, which are introduced to compute the gradient, can be also solved iteratively. The idea of iterating at the same…
In this paper, we provide a mathematical framework for improving generalization in a class of learning problems which is related to point estimations for modeling of high-dimensional nonlinear functions. In particular, we consider a…
The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory computation of gradients…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…