Duality Gap Estimation for Box Constrained Quadratic Programs via Weighted Distance Measures

碩士 === 國立成功大學 === 數學系應用數學碩博士班 === 102 === In this thesis, we estimate the gap between a box constrained quadratic program and its SDP relaxation. The problem includes the binary quadratic program as a special case and is thus in general NP-hard. Applying the saddle point theorem, we show that the du...

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Main Authors: Chih-IWeng, 翁之翊
Other Authors: Ruey-Lin Sheu
Format: Others
Language:en_US
Published: 2014
Online Access:http://ndltd.ncl.edu.tw/handle/59874691302003868414
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spelling ndltd-TW-102NCKU55070722016-03-07T04:10:56Z http://ndltd.ncl.edu.tw/handle/59874691302003868414 Duality Gap Estimation for Box Constrained Quadratic Programs via Weighted Distance Measures 利用加權距離估算帶有方塊限制二次非凸規劃之對偶間隙 Chih-IWeng 翁之翊 碩士 國立成功大學 數學系應用數學碩博士班 102 In this thesis, we estimate the gap between a box constrained quadratic program and its SDP relaxation. The problem includes the binary quadratic program as a special case and is thus in general NP-hard. Applying the saddle point theorem, we show that the duality gap can be estimated by a function $delta_{W}( heta)$ measuring a weighted distance between an affine subspace $C^*$ and some parametrized box $Lambda^{*}( heta)$. Incorporating a technique called the hyperplane arrangement in discrete geometry with various choices of parameters and weights, we are able to tighten the bound for the gap. Illustrative examples based on heuristic strategies show how a better bound can be chosen. Ruey-Lin Sheu 許瑞麟 2014 學位論文 ; thesis 68 en_US
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description 碩士 === 國立成功大學 === 數學系應用數學碩博士班 === 102 === In this thesis, we estimate the gap between a box constrained quadratic program and its SDP relaxation. The problem includes the binary quadratic program as a special case and is thus in general NP-hard. Applying the saddle point theorem, we show that the duality gap can be estimated by a function $delta_{W}( heta)$ measuring a weighted distance between an affine subspace $C^*$ and some parametrized box $Lambda^{*}( heta)$. Incorporating a technique called the hyperplane arrangement in discrete geometry with various choices of parameters and weights, we are able to tighten the bound for the gap. Illustrative examples based on heuristic strategies show how a better bound can be chosen.
author2 Ruey-Lin Sheu
author_facet Ruey-Lin Sheu
Chih-IWeng
翁之翊
author Chih-IWeng
翁之翊
spellingShingle Chih-IWeng
翁之翊
Duality Gap Estimation for Box Constrained Quadratic Programs via Weighted Distance Measures
author_sort Chih-IWeng
title Duality Gap Estimation for Box Constrained Quadratic Programs via Weighted Distance Measures
title_short Duality Gap Estimation for Box Constrained Quadratic Programs via Weighted Distance Measures
title_full Duality Gap Estimation for Box Constrained Quadratic Programs via Weighted Distance Measures
title_fullStr Duality Gap Estimation for Box Constrained Quadratic Programs via Weighted Distance Measures
title_full_unstemmed Duality Gap Estimation for Box Constrained Quadratic Programs via Weighted Distance Measures
title_sort duality gap estimation for box constrained quadratic programs via weighted distance measures
publishDate 2014
url http://ndltd.ncl.edu.tw/handle/59874691302003868414
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AT wēngzhīyì lìyòngjiāquánjùlígūsuàndàiyǒufāngkuàixiànzhìèrcìfēitūguīhuàzhīduìǒujiānxì
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