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In an effort to develop an alternative approach to traditional sparsereformulations, we will provide a new type of convex reformulation of a largeclass of stochastic quadratically constrained quadratic optimization problemsthat is similar to Burer's reformulation, but lifts the variables into acomparatively lower dimensional space. The reformulation rests on ageneralization of the set-completely positive matrix cone. This cone can thenbe approximated via inner and outer approximations in order to obtain upper andlower bounds, which potentially close the optimality gap, and hence can give acertificate of exactness for these sparse reformulations outside oftraditional, known sufficient conditions. Finally, we provide some numericalexperiments, where we asses the quality of the inner and outer approximations,thereby showing that the approximations may indeed close the optimality gap ininteresting cases.

Sparse Conic Reformulation of Structured QCQPs based on Copositive Optimization with Applications in Stochastic Optimization