arXiv subjects

Anshika

Publications and source records attributed to Anshika.

5 recordsLinked to original sources

arXiv2026

Proximal Gradient Methods for Unconstrained Set Optimization Problems with Set-Valued Maps of Finite Cardinality

This work presents two different types of proximal gradient methods, with line search and without line search, for solving unconstrained set-valued optimization problems under the lower set-less ordering relation induced by a solid cone that is convex, pointed, and closed. The objective mapping of the problem involves finitely many functions, with each one being the sum of a continuously differentiable function and a convex function that is proper and closed. We present an approach to characterize weakly minimal points of the problem with the help of weakly efficient points of a family of vector optimization problems. Thereafter, we establish a stationarity condition along with its connection with weakly minimal points of the problem under study. Based on the stationary condition, the concept of a descent direction at a non-stationary point is discussed. In view of the line search-based method, we formulate an Armijo-type line search condition and establish the existence of such a step-size. For the proposed methods, global convergence is established under mild assumptions. The convergence analysis of the proximal gradient method with line search provides a theoretical advancement over the convergence results previously established for the steepest descent method in set-valued optimization problems. In addition, we analyze the computational complexity of the proposed methods and show that both methods achieve a convergence rate of $\mathcal{O}(1/\sqrt{k})$. Numerical results are reported to test the performance of the methods in practice.

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arXiv2025

Balancing SoC in Battery Cells using Safe Action Perturbations

Managing equal charge levels in active cell balancing while charging a Li-ion battery is challenging. An imbalance in charge levels affects the state of health of the battery, along with the concerns of thermal runaway and fire hazards. Traditional methods focus on safety assurance as a trade-off between safety and charging time. Others deal with battery-specific conditions to ensure safety, therefore losing on the generalization of the control strategies over various configurations of batteries. In this work, we propose a method to learn safe battery charging actions by using a safety-layer as an add-on over a Deep Reinforcement Learning (RL) agent. The safety layer perturbs the agent's action to prevent the battery from encountering unsafe or dangerous states. Further, our Deep RL framework focuses on learning a generalized policy that can be effectively employed with varying configurations of batteries. Our experimental results demonstrate that the safety-layer based action perturbation incurs fewer safety violations by avoiding unsafe states along with learning a robust policy for several battery configurations.

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arXiv2024

Quasi-Newton Method for Set Optimization Problems with Set-Valued Mapping Given by Finitely Many Vector-Valued Functions

In this article, we propose a quasi-Newton method for unconstrained set optimization problems to find its weakly minimal solutions with respect to lower set-less ordering. The set-valued objective mapping under consideration is given by a finite number of vector-valued functions that are twice continuously differentiable. To find the necessary optimality condition for weak minimal points with the help of the proposed quasi-Newton method, we use the concept of partition and formulate a family of vector optimization problems. The evaluation of necessary optimality condition for finding the weakly minimal points involves the computation of the approximate Hessian of every objective function, which is done by a quasi-Newton scheme for vector optimization problems. In the proposed quasi-Newton method, we derive a sequence of iterative points that exhibits convergence to a point which satisfies the derived necessary optimality condition for weakly minimal points. After that, we find a descent direction for a suitably chosen vector optimization problem from this family of vector optimization problems and update from the current iterate to the next iterate. The proposed quasi-Newton method for set optimization problems is not a direct extension of that for vector optimization problems, as the selected vector optimization problem varies across the iterates. The well-definedness and convergence of the proposed method are analyzed. The convergence of the proposed algorithm under some regularity condition of the stationary points, a condition on nonstationary points, the boundedness of the norm of quasi-Newton direction, and the existence of step length that satisfies the Armijo condition are derived. We obtain a local superlinear convergence of the proposed method under uniform continuity of the Hessian approximation function.

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arXiv2024

Newton Method for Set Optimization Problems with Set-Valued Mapping of Finitely Many Vector-Valued Functions

In this paper, we propose a Newton method for unconstrained set optimization problems to find its weakly minimal solutions with respect to lower set-less ordering. The objective function of the problem under consideration is given by finitely many strongly convex twice continuously differentiable vector-valued functions. At first, with the help of a family of vector optimization problems and the Gerstewitz scalarizing function, we identify a necessary optimality condition for weakly minimal solutions of the considered problem. In the proposed Newton method, we derive a sequence of iterative points that exhibits local convergence to a point which satisfies the derived necessary optimality condition for weakly minimal points. To find this sequence of iterates, we formulate a family of vector optimization problems with the help of a partition set concept. Then, we find a descent direction for this obtained family of vector optimization problems to progress from the current iterate to the next iterate. As the chosen vector optimization problem differed across the iterates, the proposed Newton method for set optimization problems is not a straight extension of that for vector optimization problems. A step-wise algorithm of the entire process is provided. The well-definedness and convergence of the proposed method are analyzed. To establish the convergence of the proposed algorithm under some regularity condition of the stationary points, we derive three key relations: a condition of nonstationarity, the boundedness of the norm of Newton direction, and the existence of step length that satisfies the Armijo condition. We obtain the local superlinear convergence of the proposed method under uniform continuity of the Hessian and local quadratic convergence under Lipschitz continuity of the Hessian.

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arXiv2021

Generalized-Hukuhara Subdifferential Analysis and Its Application in Nonconvex Composite Optimization Problems with Interval-valued Functions

In this article, we study $gH$-subdifferential calculus of convex interval-valued functions (IVFs) and apply it in a nonconvex composite model of interval optimization problems (IOPs). It is found that the $gH$-directional derivative of maximum of finitely many comparable IVFs is the maximum of their $gH$-directional derivative. Proposed concepts of $gH$-subdifferential are observed to be useful to derive Fritz-John-type and KKT-type efficiency conditions for weak efficient solutions of IOPs. Further, we extract a necessary and sufficient condition to characterize the weak efficient solutions of nonconvex composite IOPs by applying the proposed concepts. To derive the results on $gH$-subdifferentials, the concepts of limit supremum and limit infimum with certain properties for IVFs are defined in the sequel. The whole analysis is supported by appropriate expository examples.

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