Above are papers related to the following paper: [Paper_ID] Paper #60560. 	[Title] Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, A Globally Convergent Inexact Newton Method for [Abstract] We propose an algorithm for solving systems of monotone equations which combines Newton, proximal point, and projection methodologies. An important property of the algorithm is that the whole sequence of iterates is always globally convergent to a solution of the system without any additional regularity assumptions. Moreover, under standard assumptions the local su-perlinear rate of convergence is achieved. As opposed to classical globalization strategies for Newton methods, for computing the stepsize we do not use line-search aimed at decreasing the value of some merit function. Instead, linesearch in the approximate Newton direction is used to construct an appropriate hy-perplane which separates the current iterate from the solution set. This step is followed by projecting the current iterate onto this hyperplane, which ensures global convergence of the algorithm. Computational cost of each iteration of our method is of the same order as that of the classical damped Newton method. The crucial advantage is that our method is truly globally convergent. In particular, it cannot get trapped in a stationary point of a merit function. The presented algorithm is motivated by the hybrid projection-proximal point method proposed in [25]. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #380341. 	[Title] Journal of Convex Analysis (accepted for publication) A HYBRID PROJECTION-PROXIMAL POINT ALGORITHM [Abstract] We propose a modification of the classical proximal point algorithm for finding zeroes of a maximal monotone operator in a Hilbert space. In particular, an approximate proximal point iteration is used to construct a hyperplane which strictly separates the current iterate from the solution set of the problem. This step is then followed by a projection of the current iterate onto the separating hyperplane. All information required for this projection operation is readily available at the end of the approximate proximal step, and therefore this projection entails no additional computational cost. The new algorithm allows significant relaxation of tolerance requirements imposed on the solution of proximal point subproblems, which yields a more practical framework. Weak global convergence and local linear rate of convergence are established under suitable assumptions. Additionally, presented analysis yields an alternative proof of convergence for the exact proximal point method, which allows a nice geometric interpretation, and is somewhat more intuitive than the classical proof. Please summarise all the given information.

Paper #60560 has the title `Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, A Globally Convergent Inexact Newton Method for
` and the abstract `We propose an algorithm for solving systems of monotone equations which combines Newton, proximal point, and projection methodologies. An important property of the algorithm is that the whole sequence of iterates is always globally convergent to a solution of the system without any additional regularity assumptions. Moreover, under standard assumptions the local su-perlinear rate of convergence is achieved. As opposed to classical globalization strategies for Newton methods, for computing the stepsize we do not use line-search aimed at decreasing the value of some merit function. Instead, linesearch in the approximate Newton direction is used to construct an appropriate hy-perplane which separates the current iterate from the solution set. This step is followed by projecting the current iterate onto this hyperplane, which ensures global convergence of the algorithm. Computational cost of each iteration of our method is of the same order as that of the classical damped Newton method. The crucial advantage is that our method is truly globally convergent. In particular, it cannot get trapped in a stationary point of a merit function. The presented algorithm is motivated by the hybrid projection-proximal point method proposed in [25]. 
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Question: Which category should Paper #60560 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #60560 has the title `Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, A Globally Convergent Inexact Newton Method for
` and the abstract `We propose an algorithm for solving systems of monotone equations which combines Newton, proximal point, and projection methodologies. An important property of the algorithm is that the whole sequence of iterates is always globally convergent to a solution of the system without any additional regularity assumptions. Moreover, under standard assumptions the local su-perlinear rate of convergence is achieved. As opposed to classical globalization strategies for Newton methods, for computing the stepsize we do not use line-search aimed at decreasing the value of some merit function. Instead, linesearch in the approximate Newton direction is used to construct an appropriate hy-perplane which separates the current iterate from the solution set. This step is followed by projecting the current iterate onto this hyperplane, which ensures global convergence of the algorithm. Computational cost of each iteration of our method is of the same order as that of the classical damped Newton method. The crucial advantage is that our method is truly globally convergent. In particular, it cannot get trapped in a stationary point of a merit function. The presented algorithm is motivated by the hybrid projection-proximal point method proposed in [25]. 
`.
Question: Which category should Paper #60560 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Neural_Networks