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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| Format: | Others |
| Language: | en_US |
| Published: |
2014
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| Online Access: | http://ndltd.ncl.edu.tw/handle/59874691302003868414 |
| Summary: | 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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