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The Discrete Moment Problem with Nonconvex Shape Constraints

The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with additional shape constraints that guarantee the worst-case distribution is either log-concave (LC), has an increasing failure rate (IFR), or increasing generalized failure rate (IGFR). These classes of shape constraints have not previously been studied in the literature, in part due to their inherent nonconvexities. Nonetheless, these classes are useful in practice, with applications in revenue management, reliability, and inventory control. We characterize the structure of optimal extreme point distributions under these constraints. We show, for example, that an optimal extreme point solution to a moment problem with m moments and LC shape constraints is piecewise geometric with at most m pieces. This optimality structure allows us to design an exact algorithm for computing optimal solutions in a low-dimensional space of parameters. We also leverage this structure to study a robust newsvendor problem with shape constraints and compute optimal solutions.

Ketersediaan

Informasi Detail

Judul Seri

OPERATIONS RESEARCH; Vol.69 No.1 January-February 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 279 - 296

Bahasa

English

ISBN/ISSN

-

Klasifikasi

-

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

ROBUST OPTIMIZATION
SHAPE CONSTRAINTS
MOMENT PROBLEM
REVERSE CONVEX PROGRAMMING

Info Detail Spesifik

https://doi.org/10.1287/opre.2020.1990

Pernyataan Tanggungjawab

Xi Chen, Simai He, Bo Jiang, Christopher Thomas Ryan, Teng Zhang

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