Although second-order conditions in terms of coderivative Hessians can, in general, be far from the sharpest conditions for confirming local optimality, if only that were the issue, our results show that …

The second question: How does one recognize or certify a (local) optimal solution? We answered it for LP by developing Optimality Conditions from the LP duality and Complementarity.

While extensive research has focused on its ability to achieve a globally optimal solution, there still lacks a rigorous analysis of its local optimal-ity guarantees. In this paper, we first present conditions under …

Strict local optimality in unconstrained optimization In this section, we show that testing strict local optimality in the unconstrained case is hard even for low-degree polynomials.

Hence, if there exists a polynomial-time algorithm that finds a leader’s solution that is within Euclidean distance of cn of any locally optimal leader’s solution, then we can answer the question whether α(G) …

2022年1月8日 · It states that given any solution to an optimization problem, if certain simple “local” changes can improve the solution, then one should do it. When no such improvements via local …

Optimal power flow (OPF) is a well studied optimization problem in power systems. The objective of OPF is to find a steady state operating point that minimizes the cost of electric power generation …