Continuous Equality Knapsack with Probit-Style Objectives
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866909252469129216 |
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| author | Fravel, Jamie Hildebrand, Robert Travis, Laurel |
| author_facet | Fravel, Jamie Hildebrand, Robert Travis, Laurel |
| contents | We study continuous, equality knapsack problems with uniform separable, non-convex objective functions that are continuous, antisymmetric about a point, and have concave and convex regions. For example, this model captures a simple allocation problem with the goal of optimizing an expected value where the objective is a sum of cumulative distribution functions of identically distributed normal distributions (i.e., a sum of inverse probit functions). We prove structural results of this model under general assumptions and provide two algorithms for efficient optimization: (1) running in linear time and (2) running in a constant number of operations given preprocessing of the objective function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_02237 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Continuous Equality Knapsack with Probit-Style Objectives Fravel, Jamie Hildebrand, Robert Travis, Laurel Optimization and Control We study continuous, equality knapsack problems with uniform separable, non-convex objective functions that are continuous, antisymmetric about a point, and have concave and convex regions. For example, this model captures a simple allocation problem with the goal of optimizing an expected value where the objective is a sum of cumulative distribution functions of identically distributed normal distributions (i.e., a sum of inverse probit functions). We prove structural results of this model under general assumptions and provide two algorithms for efficient optimization: (1) running in linear time and (2) running in a constant number of operations given preprocessing of the objective function. |
| title | Continuous Equality Knapsack with Probit-Style Objectives |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2211.02237 |