Sparse conic reformulation of structured QCQPs based on copositive optimization with applications in stochastic optimization
نویسندگان
چکیده
Abstract Recently, Bomze et al. introduced a sparse conic relaxation of the scenario problem two stage stochastic version standard quadratic optimization problem. When compared numerically to Burer’s classical reformulation, authors showed that there seems be almost no difference in terms solution quality, whereas time can differ by orders magnitudes. While did find very limited special case, for which reformulation and their are equivalent, satisfying explanation high quality bound was given. This article aims at shedding more light on this phenomenon give thorough theoretical account its inner workings. We argue outer approximation cannot explained traditional results relaxations based positive semidenifnite or completely matrix completion, require certain sparsity patterns characterized chordal block clique graphs respectively, put restrictions type constraint they seek sparsify. In an effort develop alternative approach, we will provide new convex large class quadratically constrained problems is similar but lifts variables into comparatively lower dimensional space. The rests generalization set-completely cone. cone then approximated via approximations order obtain upper bounds, potentially close optimality gap, hence certificate exactness these reformulations outside traditional, known sufficient conditions. Finally, some numerical experiments, where asses approximations, thereby showing may indeed gap interesting cases.
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ژورنال
عنوان ژورنال: Journal of Global Optimization
سال: 2023
ISSN: ['1573-2916', '0925-5001']
DOI: https://doi.org/10.1007/s10898-023-01283-y