Abstract Support vector machine (SVM) is one of the most important class of machine learning models and algorithms, and has been successfully applied in various fields. Nonlinear optimization plays a crucial role in SVM methodology, both in defining the machine learning models and in designing convergent and efficient algorithms for large-scale training problems. In this paper we present the convex programming problems underlying SVM focusing on supervised binary classification. We analyze the most important and used optimization methods for SVM training problems, and we discuss how the properties of these problems can be incorporated in designing useful algorithms.

Veronica Piccialli

Marco Sciandrone

Annals of Operations Research

《运筹学年鉴》发表同行评审的原创文章，涉及运筹学的关键方面，包括理论、实践和计算。该杂志发表完整的研究文章、简短的笔记、展览和调查、关于计算研究的报告以及展示新的和创新的实际应用的案例研究。除了常规问题外，该杂志还定期出版专注于特定领域的特刊运筹学，从高度理论到算法和应用。这些卷有一名或多名客座编辑，他们负责收集论文并监督审稿过程。

The Annals of Operations Research publishes peer-reviewed original articles covering key aspects of operations research, including theory, practice, and computation. The journal accepts full research papers, short notes, exhibitions and surveys, as well as case studies showcasing new and innovative practical applications. In addition to regular issues, the Annals of Operations Research also regularly publishes special issues focused on specific areas, ranging from highly theoretical to algorithmic and applied topics. These volumes are overseen by one or more guest editors who are responsible for collecting papers and managing the review process.

《运筹学年鉴》发表经过同行评审的原创文章，涵盖运筹学的关键领域，包括理论、实践和计算。该杂志接受完整的研究论文、简短的笔记、展览和调查报告，以及展示新颖和创新实际应用的案例研究。除了常规期刊外，《运筹学年鉴》还定期出版专注于特定领域的特刊，内容从高度理论到算法和应用不等。这些特刊由一名或多名客座编辑负责，他们负责收集论文并监督审稿过程。

Nonlinear optimization and support vector machines

This paper presents the convex programming problems underlying SVM focusing on supervised binary classification and analyzes the most important and used optimization methods for SVM training problems, and discusses how the properties of these problems can be incorporated in designing useful algorithms.

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管理学, 运筹学与管理科学	3

Nonlinear optimization and support vector machines

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Category	Quartile
OPERATIONS RESEARCH & MANAGEMENT SCIENCE	1