Exact Optimization: Part I
Abstract
Nonlinear programming is explicitly analyzed via a novel perspective/method and from a bottom-up manner. The philosophy is based on the recent findings on convex quadratic equation (CQE), which help clarify a geometric interpretation that relates CQE to convex quadratic function (CQF). More specifically, regarding the solvability of CQE, its necessary and sufficient condition as well as a unified parameterization of all the solutions has recently been analytically formulated. Moving forward, the understanding of CQE is utilized to describe the geometric structure of CQF, and the CQE-CQF relation. All these results are shown closely related to a basis in the optimization literature, namely quadratic programming (QP). For the first time from this viewpoint, the QPs subject to equality, inequality, equality-and-inequality, and extended constraints can be algebraically solved in derivative-free closed formulae, respectively. All the results are derived without knowing a feasible point, a priori and any time during the process.
Cite
@article{arxiv.1906.00177,
title = {Exact Optimization: Part I},
author = {Li-Gang Lin and Yew-Wen Liang},
journal= {arXiv preprint arXiv:1906.00177},
year = {2022}
}
Comments
This manuscript is only preliminary and still growing. Therefore, with expectations, we deeply appreciate all kinds of input. It is worth noting that, with gratitude for all the editorial effort, we complied with the comment/instruction to divide this manuscript into different journals and have been working on the sequels