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Non-convex optimization

Non-convex optimizationIssam LaradjiStrongly Convex f(x)xObjective functionStrongly Convex Assumptionsf(x)xObjective functionGradient Lipschitz continuousStrongly convexStrongly Convex Assumptionsf(x)xObjective functionGradient Lipschitz continuousStrongly convexRandomized coordinate descentNon-strongly Convex optimizationAssumptionsGradient Lipschitz continuousConvergence rateCompared to the strongly convex convergence rateNon-strongly Convex optimizationNon-Strongly Convex AssumptionsObjective functionLipschitz continuousRestricted secant inequalityRandomized coordinate descentInvex functions (a generalization of convex function)

Sample noise r uniformly from unit sphere Escapes saddle points but step size is difficult to determine Momentum can help escape saddle points (rolling ball) Matrix completion problem [De Sa et al. 2015] Global non-convex optimization

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