by 謝叔宴 | 2021-08-26 15:28:07
Title : Exact Optimization: A Status Report with Future Promises
The nonlinear programming, from a bottom-up manner, is being explicitly analyzed via a novel perspective/method. More specifically, the up-to-date optimization literature can be classified by three levels: (1) equality-constrained quadratic programming (QP); (2) linear equality-constrained optimization problem with twice-differentiable objective, as solved using Newton’s method by reducing it to a sequence of equality-constrained QPs; and, after further imposing inequality constraints, (3) interior-point methods, which reduce the problem to a sequence of (2). For the first time from the proposed viewpoint toward exact optimization, (1) together with the QPs subject to inequality, equality-and-inequality, and extended constraints, respectively, can be algebraically solved in derivative-free closed formulae. All the results are derived without knowing a feasible point, a priori and any time during the process. Moreover, a variety of practical validations, evaluations, and comparisons with benchmark literature (such as MATLAB®) are provided to demonstrate the superiority of the proposed method, notably the enhanced computational efficiency. Meanwhile, much more comparisons/interactions with extensive (numerical) solvers can be more efficiently obtained by virtue of collaborations. Remarkably, the very first idea along this research direction was originated in Taiwan, the progress so far is obtained by Taiwanese only, and thus it is expected that all the main observations will be Taiwan-marked before reaching out to diverse applications in the world.
Time: Oct. 6 (Wed.), 1:40 p.m., 2021
Place: Room 212, Department of Mathematics, NTNU
Tea Time: Oct. 6 (Wed.), 1:20 p.m., 2021
Tea Place: Room 104, Department of Mathematics, NTNU
URL of class：https://meet.google.com/ngz-pnbq-ghg
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Source URL: https://cantor.math.ntnu.edu.tw/index.php/2021/08/26/001-23-2/
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