• Dharminder Singh
• Dr.Amanpreet Singh

A novel smooth penalty function method is introduced, which eliminates the need for dual and slack implicit variables in formulating constrained optimization conditions. This method features new active and loss functions that independently and adaptively address the violation of each constraint. By minimizing the proposed penalty function unconstrained, a solution to the original optimization problem is achieved. The derived constrained optimization conditions rely solely on the primal variable and extend to encompass the canonical Karush-Kuhn-Tucker (KKT) conditions within a broader framework. The derivatives of the proposed loss functions concerning the constraint functions can be interpreted as Lagrange multipliers of the traditional Lagrangian function. Additionally, the method reveals the inclusion of first-order Hessian information, contrasting with existing works where classical Lagrange Hessians only incorporate second-order derivatives. Finally, numerical examples, including medium-scale stress-constrained topology optimization and scenario-based reliability design problems, are provided to illustrate the effectiveness of the proposed methodology.

A Smooth Exact Penalty Function Approach for Constrained Optimization with Applications in Stress-Constrained Topology Optimization and Scenario-Based Reliability Design

"A Smooth Exact Penalty Function Approach for Constrained Optimization with Applications in Stress-Constrained Topology Optimization and Scenario-Based Reliability Design", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 2, page no.18-21, February-2019, Available :http://www.jetir.org/papers/JETIR1902H05.pdf

"A Smooth Exact Penalty Function Approach for Constrained Optimization with Applications in Stress-Constrained Topology Optimization and Scenario-Based Reliability Design", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 2, page no. pp18-21, February-2019, Available at : http://www.jetir.org/papers/JETIR1902H05.pdf