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Parabolic Relaxation for Quadratically-constrained Quadratic Programming -- Part II: Theoretical & Computational Results

arXiv 2208.03625 ↗First posted 7 Aug 2022math.OC cs.LGcited by 0

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Abstract (arXiv)

In the first part of this work [32], we introduce a convex parabolic relaxation for quadratically-constrained quadratic programs, along with a sequential penalized parabolic relaxation algorithm to recover near-optimal feasible solutions. In this second part, we show that starting from a feasible solution or a near-feasible solution satisfying certain regularity conditions, the sequential penalized parabolic relaxation algorithm convergences to a point which satisfies Karush-Kuhn-Tucker optimality conditions. Next, we present numerical experiments on benchmark non-convex QCQP problems as well as large-scale instances of system identification problem demonstrating the efficiency of the proposed approach.

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References · 20

  1. 2018Semidefinite relaxations for certifying robustness to adversarial examplescited by 179
  2. 2019Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programmingcited by 101
  3. 2016The non-convex Burer-Monteiro approach works on smooth semidefinite programscited by 46
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  10. 2016A System Level Approach to Controller Synthesiscited by 9
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  12. 2018Convergence Rate of Block-Coordinate Maximization Burer-Monteiro Method for Solving Large SDPscited by 7
8 more
  1. 2015A bounded degree SOS hierarchy for polynomial optimizationcited by 5
  2. 2015Optimization over Structured Subsets of Positive Semidefinite Matrices via Column Generationcited by 2
  3. 2017Separable and Localized System Level Synthesis for Large-Scale Systemscited by 2
  4. 2017The many faces of degeneracy in conic optimizationcited by 2
  5. 2018Convex Relaxation of Bilinear Matrix Inequalities Part II: Applications to Optimal Control Synthesiscited by 2
  6. 2013Strong duality in conic linear programming: facial reduction and extended dualscited by 1
  7. 2015Sum of Squares Basis Pursuit with Linear and Second Order Cone Programmingcited by 1
  8. 2018A Two-Step Pre-Processing for Semidefinite Programmingcited by 1

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