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Convex Analysis and Optimization with Submodular Functions: a Tutorial

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arxiv 1010.4207 v2 pith:46QFWFVY submitted 2010-10-20 cs.LG math.OCstat.ML

Francis Bach (INRIA Rocquencourt , LIENS) This is my paper · ORCID
classification cs.LGmath.OCstat.ML
keywords functionsconvexsubmodularanalysiscomputerset-functionstutorialappear
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Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role, similar to convex functions on vector spaces. In this tutorial, the theory of submodular functions is presented, in a self-contained way, with all results shown from first principles. A good knowledge of convex analysis is assumed.

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Cited by 2 Pith papers

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  1. Partitioning and Observability in Linear Systems via Submodular Optimization

    eess.SY 2025-05 reject novelty 6.0 of 10

    A framework that partitions linear systems to maximize observability Gramian metrics, then places sensors under partition-matroid constraints via a continuous greedy algorithm.

  2. V2C-CBM: Building Concept Bottlenecks with Vision-to-Concept Tokenizer

    cs.CV 2025-01 conditional novelty 5.0 of 10

    A concept bottleneck model that discovers class concepts directly from images by quantizing them into nearest common words in CLIP space, matching or beating LLM-generated concept bottlenecks without using LLMs.

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