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Disciplined quasiconvex programming

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Abstract

We present a composition rule involving quasiconvex functions that generalizes the classical composition rule for convex functions. This rule complements well-known rules for the curvature of quasiconvex functions under increasing functions and pointwise maximums. We refer to the class of optimization problems generated by these rules, along with a base set of quasiconvex and quasiconcave functions, as disciplined quasiconvex programs. Disciplined quasiconvex programming generalizes disciplined convex programming, the class of optimization problems targeted by most modern domain-specific languages for convex optimization. We describe an implementation of disciplined quasiconvex programming that makes it possible to specify and solve quasiconvex programs in CVXPY 1.0.

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Acknowledgements

The authors thank Steven Diamond for many useful discussions.

Funding

A. Agrawal is supported by a Stanford Graduate Fellowship.

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Authors and Affiliations

  1. Department of Electrical Engineering, Stanford University, 450 Serra Mall, Stanford, CA, 94305, USA

    Akshay Agrawal & Stephen Boyd

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  1. Akshay Agrawal
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  2. Stephen Boyd
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Correspondence to Akshay Agrawal.

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Agrawal, A., Boyd, S. Disciplined quasiconvex programming. Optim Lett 14, 1643–1657 (2020). https://doi.org/10.1007/s11590-020-01561-8

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  • DOI: https://doi.org/10.1007/s11590-020-01561-8

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