human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "linear convergence on positively homogeneous functions of a comparison based step size adaptive randomized search the 1 1 es with generalized one fifth success rule"
  Abstract: In the context of unconstraint numerical optimization, this paper investigates the global linear convergence of a simple probabilistic derivative-free optimization algorithm (DFO). The algorithm samples a candidate solution from a standard multivariate normal distribution scaled by a step-size and centered in the current solution. This solution is accepted if it has a better objective function value than the current one. Crucial to the algorithm is the adaptation of the step-size that is done in order to maintain a certain probability of success. The algorithm, already proposed in the 60's, is a generalization of the well-known Rechenberg's $(1+1)$ Evolution Strategy (ES) with one-fifth success rule which was also proposed by Devroye under the name compound random search or by Schumer and Steiglitz under the name step-size adaptive random search. In addition to be derivative-free, the algorithm is function-value-free: it exploits the objective function only through comparisons. It belongs to the class of comparison-based step-size adaptive randomized search (CB-SARS). For the convergence analysis, we follow the methodology developed in a companion paper for investigating linear convergence of CB-SARS: by exploiting invariance properties of the algorithm, we turn the study of global linear convergence on scaling-invariant functions into the study of the stability of an underlying normalized Markov chain (MC). We hence prove global linear convergence by studying the stability (irreducibility, recurrence, positivity, geometric ergodicity) of the normalized MC associated to the $(1+1)$-ES. More precisely, we prove that starting from any initial solution and any step-size, linear convergence with probability one and in expectation occurs. Our proof holds on unimodal functions that are the composite of strictly increasing functions by positively homogeneous functions with degree $\alpha$ (assumed also to be continuously differentiable). This function class includes composite of norm functions but also non-quasi convex functions. Because of the composition by a strictly increasing function, it includes non continuous functions. We find that a sufficient condition for global linear convergence is the step-size increase on linear functions, a condition typically satisfied for standard parameter choices. While introduced more than 40 years ago, we provide here the first proof of global linear convergence for the $(1+1)$-ES with generalized one-fifth success rule and the first proof of linear convergence for a CB-SARS on such a class of functions that includes non-quasi convex and non-continuous functions. Our proof also holds on functions where linear convergence of some CB-SARS was previously proven, namely convex-quadratic functions (including the well-know sphere function).

Connected through hyperedge HE-1 (induced by source paper "drift theory in continuous search spaces expected hitting time of the 1 1 es with 1 5 success rule"):
  with members:
    - "general drift analysis with tail bounds"
    - "multiplicative drift analysis"

Connected through hyperedge HE-2 (induced by source paper "optimal parameter choices through self adjustment applying the 1 5 th rule in discrete settings"):
  with members:
    - "adaptive population models for offspring populations and parallel evolutionary algorithms"

Connected through hyperedge HE-3 (induced by source paper "linear convergence of comparison based step size adaptive randomized search via stability of markov chains"):
  with members:
    - "cumulative step size adaptation on linear functions"
    - "on the complexity of bandit and derivative free stochastic convex optimization"
    - "convergence of the continuous time trajectories of isotropic evolution strategies on monotonic c 2 composite functions"

Question: Please tell me which class the center node belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.NA(Numerical Analysis)