{"ID":2863549,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.24689","arxiv_id":"2509.24689","title":"$\\mathcal{KL}$ and Lyapunov Approaches for Discrete-time Peak Computation Problems","abstract":"In this paper, we propose a method to solve discrete-time peak computation problems (DPCPs for short). DPCPs are optimization problems that consist of maximizing a function over the reachable values set of a discrete-time dynamical system. The optimal value of a DPCP can be rewritten as the supremum of the sequence of optimal values. Previous results provide general techniques for computing the supremum of a real sequence from a well-chosen pair of a strictly increasing continuous function on [0,1] and a positive scalar in (0,1). In this paper, we exploit the specific structure of the optimal value of the DPCP to construct such a pair from classical tools from stability theory: $\\mathcal{KL}$ certificate and Lyapunov functions.","short_abstract":"In this paper, we propose a method to solve discrete-time peak computation problems (DPCPs for short). DPCPs are optimization problems that consist of maximizing a function over the reachable values set of a discrete-time dynamical system. The optimal value of a DPCP can be rewritten as the supremum of the sequence of...","url_abs":"https://arxiv.org/abs/2509.24689","url_pdf":"https://arxiv.org/pdf/2509.24689v1","authors":"[\"Assalé Adjé\"]","published":"2025-09-29T12:25:51Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.DS\"]","methods":"[]","has_code":false}