A bundle-type method for nonsmooth DC programs

IF 1.8 3区数学 Q1 Mathematics

Journal of Global Optimization Pub Date : 2023-09-25 DOI:10.1007/s10898-023-01325-5

Christian Kanzow, Tanja Neder

引用次数: 0

Abstract

Abstract A bundle method for minimizing the difference of convex (DC) and possibly nonsmooth functions is developed. The method may be viewed as an inexact version of the DC algorithm, where each subproblem is solved only approximately by a bundle method. We always terminate the bundle method after the first serious step. This yields a descent direction for the original objective function, and it is shown that a stepsize of at least one is accepted in this way. Using a line search, even larger stepsizes are possible. The overall method is shown to be globally convergent to critical points of DC programs. The new algorithm is tested and compared to some other solution methods on several examples and realistic applications.

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非光滑直流规划的束型方法

摘要提出了一种求凸函数和可能的非光滑函数之差最小化的束法。该方法可以看作是DC算法的不精确版本，其中每个子问题只能通过捆绑方法近似地解决。我们总是在第一个重要步骤之后终止bundle方法。这就得到了原始目标函数的下降方向，并证明了在这种方式下，步长至少为1是可以接受的。使用行搜索，甚至可以使用更大的步长。结果表明，该方法全局收敛于直流规划的临界点。通过几个算例和实际应用对新算法进行了测试和比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Global Optimization 数学-应用数学

CiteScore

0.10

自引率

5.60%

发文量

137

审稿时长

6 months

期刊介绍： The Journal of Global Optimization publishes carefully refereed papers that encompass theoretical, computational, and applied aspects of global optimization. While the focus is on original research contributions dealing with the search for global optima of non-convex, multi-extremal problems, the journal’s scope covers optimization in the widest sense, including nonlinear, mixed integer, combinatorial, stochastic, robust, multi-objective optimization, computational geometry, and equilibrium problems. Relevant works on data-driven methods and optimization-based data mining are of special interest. In addition to papers covering theory and algorithms of global optimization, the journal publishes significant papers on numerical experiments, new testbeds, and applications in engineering, management, and the sciences. Applications of particular interest include healthcare, computational biochemistry, energy systems, telecommunications, and finance. Apart from full-length articles, the journal features short communications on both open and solved global optimization problems. It also offers reviews of relevant books and publishes special issues.