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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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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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.
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Ruey-Lin Sheu |
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Ruey-Lin Sheu Chih-IWeng 翁之翊 |
author |
Chih-IWeng 翁之翊 |
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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 |
work_keys_str_mv |
AT chihiweng dualitygapestimationforboxconstrainedquadraticprogramsviaweighteddistancemeasures AT wēngzhīyì dualitygapestimationforboxconstrainedquadraticprogramsviaweighteddistancemeasures AT chihiweng lìyòngjiāquánjùlígūsuàndàiyǒufāngkuàixiànzhìèrcìfēitūguīhuàzhīduìǒujiānxì AT wēngzhīyì lìyòngjiāquánjùlígūsuàndàiyǒufāngkuàixiànzhìèrcìfēitūguīhuàzhīduìǒujiānxì |
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1718199111919861760 |