MathDB7 problems
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The positive-cycle conjecture for determinant constraints and bound tightening in ACOPF
In an ACOPF relaxation, higher-order determinant constraints provide lower bounds on power loss, while bound tightening updates the variable bounds used by the relaxation. Positive…
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The scheduled-asynchronous algorithm's convergence-rate conjecture
Let Algorithm denote the scheduled-asynchronous distributed algorithm for optimal power flow, and let denote the iteration count. Convergence-rate conjecture. Based on the bipa…
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Avoidance of critical subspaces and nonpathological price profiles
Nonpathological-price-profile conjecture. It is unlikely that the price profile matches the critical subspaces in $$ ; consequently, pathological price profiles are unlikely to occ…
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Typical exactness of the SOC relaxation for the hybrid transmission grid architecture
Typical-exactness conjecture. The price profiles in (28) are pathological only in exceptional cases; consequently, the SOC relaxation is typically exact for the hybrid transmission…
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Higher-order moment constraints for general OPF cost functions
In an optimal power flow problem, consider more general cost functions than active power loss minimization and moment relaxations with moment constraints imposed at buses. Computat…
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The normal-operating-conditions conjecture for SDP relaxation exactness in OPF
Normal-operating-conditions conjecture. Under normal operating conditions, the SDP relaxation is tight.
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Lavaei–Low conjecture on exact convex relaxation of optimal power flow
Lavaei–Low conjecture. The convex relaxation of the optimal power flow problem is always tight for general power networks.