MathDB5 problems
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The conjecture that Gaussian flow may get stuck in local minima while CBO is more robust
Let GF denote the Gaussian gradient flow method and CBO the consensus-based optimization method for approximating Gaussian mixture target distributions, with multiple particles use…
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Extension of consensus-based optimization convergence to time-dependent parameters
Time-dependent-parameter convergence conjecture. The convergence results should extend to this setting, yielding a bound
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A refinement of the CH error bound independent of the time step
CH error-bound refinement conjecture. A refinement of the quantitative Laplace principle may allow the error in this estimate to be controlled just through and…
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Conjecture that potential-induced stochasticity explains improved solution quality
The experiments compare optimization dynamics with and without interaction in parameter space, using potentials whose choice affects the resulting solutions. Potential-induced stoc…
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Conjecture on removing well-preparation for consensus-based optimization on the sphere
Let be a cost function on the sphere and let the initial datum be an arbitrary probability distribution, without assuming the well-preparation condition. Well-preparat…