{"ID":2866471,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.19919","arxiv_id":"2509.19919","title":"A twice continuously differentiable penalty function for nonlinear semidefinite programming problems and its application","abstract":"This paper presents a twice continuously differentiable penalty function for nonlinear semidefinite programming problems. In some optimization methods, such as penalty methods and augmented Lagrangian methods, their convergence property can be ensured by incorporating a penalty function into them, and hence several types of penalty functions have been proposed. In particular, these functions are designed to apply optimization methods to find first-order stationary points. Meanwhile, in recent years, second-order sequential optimality, such as Approximate Karush-Kuhn-Tucker2 (AKKT2) and Complementarity AKKT2 (CAKKT2) conditions, has been introduced, and the development of methods for such second-order stationary points would be required in future research. However, existing well-known penalty functions have low compatibility with such methods because they are not twice continuously differentiable. In contrast, the proposed function is expected to have a high affinity for methods to find second-order stationary points. To verify the high affinity, we also present a practical penalty method to find points that satisfy the AKKT and CAKKT conditions by exploiting the proposed function and show their convergence properties.","short_abstract":"This paper presents a twice continuously differentiable penalty function for nonlinear semidefinite programming problems. In some optimization methods, such as penalty methods and augmented Lagrangian methods, their convergence property can be ensured by incorporating a penalty function into them, and hence several typ...","url_abs":"https://arxiv.org/abs/2509.19919","url_pdf":"https://arxiv.org/pdf/2509.19919v1","authors":"[\"Yuya Yamakawa\"]","published":"2025-09-24T09:21:09Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}