Related papers: Are Near Earth Objects the Key to Optimization The…
This study introduces an approach to obtain a neighboring extremal optimal control (NEOC) solution for a closed-loop optimal control problem, applicable to a wide array of nonlinear systems and not necessarily quadratic performance indices.…
In this paper, we present a novel Newton-based extremum seeking controller for the solution of multivariable model-free optimization problems in static maps. Unlike existing asymptotic and fixed-time results in the literature, we present a…
In this note, we revisit the problem of flow approximation properties of neural ordinary differential equations (NODEs). The approximation properties have been considered as a flow controllability problem in recent literature. The neural…
We consider the problem of choosing prices of a set of products so as to maximize profit, taking into account self-elasticity and cross-elasticity, subject to constraints on the prices. We show that this problem can be formulated as…
Proximal distance algorithms combine the classical penalty method of constrained minimization with distance majorization. If $f(\boldsymbol{x})$ is the loss function, and $C$ is the constraint set in a constrained minimization problem, then…
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…
Proximal Policy Optimization (PPO) is among the most widely used deep reinforcement learning algorithms, yet its theoretical foundations remain incomplete. Most importantly, convergence and understanding of fundamental PPO advantages remain…
This paper proposes novel gradient-flow schemes that yield convergence to the optimal point of a convex optimization problem within a \textit{fixed} time from any given initial condition for unconstrained optimization, constrained…
The problem of locating the global optimum of functions is studied in a dynamic setting. The dynamics of simple multistable systems under the influence of chaotic forcing is investigated. When the magnitude of the forcing signal decays…
The ability of the Quantum Approximate Optimization Algorithm (QAOA) to deliver a quantum advantage on combinatorial optimization problems is still unclear. Recently, a scaling advantage over a classical solver was postulated to exist for…
In probability theory and statistics notions of correlation among random variables, decay of correlation, and bias-variance trade-off are fundamental. In this work we introduce analogous notions in optimization, and we show their usefulness…
Missions to near-Earth objects (NEOs) are key destinations in NASA's new "Flexible Path" approach. NEOs are also of interest for science, for the hazards they pose, and for their resources. We emphasize the importance of ultra-low delta-v…
Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control and dynamic…
Fair resource allocation is a fundamental optimization problem with applications in operations research, networking, and economic and game theory. Research in these areas has led to the general acceptance of a class of $\alpha$-fair utility…
In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…
Bayesian optimization (BO) is effective for expensive black-box problems but remains challenging in high dimensions. We propose NeST-BO, a curvature-aware local BO method that targets a (modified) Newton step by jointly learning gradient…
Machine learning problems such as neural network training, tensor decomposition, and matrix factorization, require local minimization of a nonconvex function. This local minimization is challenged by the presence of saddle points, of which…
Visual object tracking is one of the major challenges in the field of computer vision. Correlation Filter (CF) trackers are one of the most widely used categories in tracking. Though numerous tracking algorithms based on CFs are available…
This contribution contains a review of the role of the three-sphere free energy F in recent developments related to the F-theorem and F-maximization. The F-theorem states that for any Lorentz-invariant RG trajectory connecting a conformal…
Neural networks have recently been employed as material discretizations within adjoint optimization frameworks for inverse problems and topology optimization. While advantageous regularization effects and better optima have been found for…