Intractability of approximate multi-dimensional nonlinear optimization on independence systems

Jon Lee; Shmuel Onn; Robert Weismantel

doi:10.1016/j.disc.2011.01.029

Intractability of approximate multi-dimensional nonlinear optimization on independence systems

Jon Lee, Shmuel Onn, Robert Weismantel

Data and Decision Sciences

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We consider optimization of nonlinear objective functions that balance d linear criteria over n-element independence systems presented by linear-optimization oracles. For d=1, we have previously shown that an r-best approximate solution can be found in polynomial time. Here, using an extended ErdsKoRado theorem of Frankl, we show that for d=2, finding a ρn-best solution requires exponential time.

Original language	English
Pages (from-to)	780-783
Number of pages	4
Journal	Discrete Mathematics
Volume	311
Issue number	8-9
DOIs	https://doi.org/10.1016/j.disc.2011.01.029
State	Published - 6 May 2011

Keywords

ErdsKoRado
Inapproximability
Nonlinear discrete optimization

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2011.01.029

Cite this

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abstract = "We consider optimization of nonlinear objective functions that balance d linear criteria over n-element independence systems presented by linear-optimization oracles. For d=1, we have previously shown that an r-best approximate solution can be found in polynomial time. Here, using an extended ErdsKoRado theorem of Frankl, we show that for d=2, finding a ρn-best solution requires exponential time.",

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AU - Weismantel, Robert

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N2 - We consider optimization of nonlinear objective functions that balance d linear criteria over n-element independence systems presented by linear-optimization oracles. For d=1, we have previously shown that an r-best approximate solution can be found in polynomial time. Here, using an extended ErdsKoRado theorem of Frankl, we show that for d=2, finding a ρn-best solution requires exponential time.

AB - We consider optimization of nonlinear objective functions that balance d linear criteria over n-element independence systems presented by linear-optimization oracles. For d=1, we have previously shown that an r-best approximate solution can be found in polynomial time. Here, using an extended ErdsKoRado theorem of Frankl, we show that for d=2, finding a ρn-best solution requires exponential time.

KW - ErdsKoRado

KW - Inapproximability

KW - Nonlinear discrete optimization

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DO - 10.1016/j.disc.2011.01.029

M3 - مقالة

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VL - 311

SP - 780

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JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 8-9

ER -

Intractability of approximate multi-dimensional nonlinear optimization on independence systems

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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