Convex quadratically constrained quadratic program

Asked 10 years, 10 months ago. Active 9 months ago. Viewed 2k times. Improve this question. Rodrigo de Azevedo 2, 3 3 gold badges 13 13 silver badges 29 29 bronze badges. Add a comment. Active Oldest Votes. Improve this answer. Kristal Cantwell Kristal Cantwell 6, 1 1 gold badge 21 21 silver badges 42 42 bronze badges. From the wiki, solving the general can be NP-hard. I'm wondering if there are some other simpler yet still general cases that can be solved in polynomial time.

The small-signal stability is an integral part of the power system security analysis. The introduction of renewable source related uncertainties is making the stability assessment difficult as the … Expand. Convex relaxations of non-convex mixed integer quadratically constrained programs: extended formulations.

Mathematics, Computer Science. View 1 excerpt, references background. Rank-constrained semidefinite program for unit commitment. Abstract Unit Commitment UC is a combinatorial optimization problem that can be posed as minimizing a quadratic objective function under quadratic constraints. This paper presents a solution to UC … Expand.

Semi-definite programming-based method for security-constrained unit commitment with operational and optimal power flow constraints. Considering the economics and securities for the operation of a power system, a semi-definite programming SDP model for the security-constrained unit commitment SCUC problem is described here, … Expand.

Highly Influential. View 3 excerpts, references background. New algorithms for nonlinear generalized disjunctive programming. Theory Appl. Pakazad, S. Control 63 4 , — Rabaste, O. Article Google Scholar. Rockafellar, R.

Princeton University Press, Princeton Google Scholar. Download references. In addition, we would like to thank Purdue Rosen Center for Advanced Computing for providing the computing resources and technical support. You can also search for this author in PubMed Google Scholar.

Correspondence to Run Chen. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. We first prove the inequality The final piece to derive inequality 24 is to utilize Lemma 3.

By Lemma 3 , we have that. Adding the three inequalities 51 , 52 and 54 yields the inequality 24 in Proposition 1. By 22a in Lemma 2 , we know that. Adding the two inequalities 57 and 60 leads to the second inequality, 25 , in Proposition 1. By adding the two inequalities 24 and 25 in Proposition 1 , we have that. Applying 64 on a yields. Applying 64 to 74 yields. We first bound. Applying 64 to 81 yields. Applying 64 to 86 yields that. Applying 64 , we have that.

Applying 64 on the above equality leads to. Taking the limit on both sides of yields:. Then implies that. Since we have argued after Eq. Reprints and Permissions.