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Task vector composition has emerged as a promising paradigm for editing pre-trained models, enabling model merging through addition and unlearning through subtraction. Fine-tuning in the tangent space of a pre-trained model (linear…

Non-convex functional constrained optimization problems have gained substantial attention in machine learning and data science, addressing broad requirements that typically go beyond the often performance-centric objectives. An influential…

This work explores a novel perspective on solving nonconvex and nonsmooth optimization problems by leveraging sampling based methods. Instead of treating the objective function purely through traditional (often deterministic) optimization…

We introduce a novel approach addressing global analysis of a difficult class of nonconvex-nonsmooth optimization problems within the important framework of Lagrangian-based methods. This genuine nonlinear class captures many problems in…

This tutorial paper provides an introduction to recently developed tools for machine learning, especially learning dynamical systems (system identification), with stability and robustness constraints. The main ideas are drawn from…

We consider adaptive control problem in presence of nonlinear parametrization of uncertainties in the model. It is shown that despite traditional approaches require for domination in the control loop during adaptation, it is not often…

The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining…

In this paper, we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints are locally smooth. For solving this problem, we propose a…

Motivated by robotic trajectory optimization problems we consider the Augmented Lagrangian approach to constrained optimization. We first propose an alternative augmentation of the Lagrangian to handle the inequality case (not based on…

Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables.…

We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key idea is to develop a new control-theoretic regularizer for dynamics fitting rooted in the notion of…

Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study…

Optimization problems involving the minimization of a finite sum of smooth, possibly non-convex functions arise in numerous applications. To achieve a consensus solution over a network, distributed optimization algorithms, such as…

Gradient Langevin dynamics and a variety of its variants have attracted increasing attention owing to their convergence towards the global optimal solution, initially in the unconstrained convex framework while recently even in convex…

Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…

Some metric and graphical regularity properties of generalized constraint systems are investigated. Then, these properties are applied in order to penalize (in the sense of Clarke) various scalar and vector optimization problems. This…

An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear…

Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…

This paper presents a strictly convex chance-constrained stochastic control framework that accounts for uncertainty in control specifications such as reference trajectories and operational constraints. By jointly optimizing control inputs…

Sparsity-based methods are widely used in machine learning, statistics, and signal processing. There is now a rich class of structured sparsity approaches that expand the modeling power of the sparsity paradigm and incorporate constraints…