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作者：Khanh, Pham Duy; Khoa, Vu Vinh Huy; Mordukhovich, Boris S.; Phat, Vo Thanh
作者单位：Wayne State University; University of North Dakota Grand Forks
摘要：The paper is devoted to a systematic study and characterizations of notions of local maximal monotonicity and their strong counterparts for set-valued operators that appear in variational analysis, optimization, and their applications. We obtain novel resolvent characterizations of these notions together with efficient conditions for their preservation under summation in broad infinite-dimensional settings. Further characterizations of these notions are derived by using generalized differentia...
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作者：Ahmadi, Amir Ali; Chaudhry, Abraar; Dibek, Cemil
作者单位：Princeton University; University System of Georgia; Georgia Institute of Technology; Koc University
摘要：We introduce a family of symmetric convex bodies called generalized ellipsoids of degree d (GE-ds), with ellipsoids corresponding to the case of d = 0. Generalized ellipsoids (GEs) retain many geometric, algebraic, and algorithmic properties of ellipsoids. We show that the conditions that the parameters of a GE must satisfy can be checked in strongly polynomial time and that one can search for GEs of a given degree by solving a semidefinite program whose size grows only linearly with dimension...
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作者：Yang, Shuoguang; Truong, Van-Anh
作者单位：Hong Kong University of Science & Technology; Columbia University
摘要：We propose the analysis of the online learning problem for independent cascade (IC) models under node-level feedback. These models have widespread applications in modern social networks. Existing works for IC models have only shed light on edge-level feedback models, where the agent knows the explicit outcome of every observed edge. Little is known about node-level feedback models where only combined outcomes for sets of edges are observed; in other words, the realization of each edge is censo...
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作者：Sentenac, Flore; Noiry, Nathan; Lerasle, Matthieu; Perchet, Vianney; Menard, Laurent
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Institut Polytechnique de Paris; ENSAE Paris; Institut Polytechnique de Paris; ENSAE Paris
摘要：We investigate online maximum cardinality matching, a central problem in ad allocation. In this problem, users are revealed sequentially, and each new user can be paired with any previously unmatched campaign that it is compatible with. Despite the limited theoretical guarantees, the greedy algorithm, which matches incoming users with any available campaign, exhibits outstanding performance in practice. Some theoretical support for this practical success has been established in specific classe...
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作者：Ahn, Dohyun; Zheng, Lewen
作者单位：Chinese University of Hong Kong
摘要：We consider the problem of estimating the expectation over a convex polyhedron specified by a set of linear inequalities. This problem encompasses a multitude of financial applications, including systemic risk quantification, exotic option pricing, and portfolio management. We particularly focus on the case where the target event is rare, which corresponds to extreme systemic failures, deep out-of-the-money options, and high target returns in the aforementioned applications, respectively. This...
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作者：Tran-Dinh, Quoc; Luo, Yang
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine
摘要：In this paper, we develop two new randomized block-coordinate optimistic gradient algorithms to approximate a solution of nonlinear equations in large-scale settings, which are known as root-finding problems. Our first algorithm is nonaccelerated with constant step sizes and achieves a O(1/k) best-iterate convergence rate on E[& Vert;Gxk & Vert;2] when the underlying operator G is Lipschitz continuous and possesses a weak Minty solution, in which E[] is the expectation and k is the iteration c...
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作者：Assumpcao, Henrique; Coutinho, Gabriel
作者单位：Universidade Federal de Minas Gerais
摘要：We use semidefinite programming to bound the fractional cut-cover parameter of graphs in association schemes in terms of their smallest eigenvalue. We also extend the equality cases of a primal-dual inequality involving the Goemans-Williamson semidefinite program, which approximates MAXCUT, to graphs in certain coherent configurations. Moreover, we obtain spectral bounds for MAX 2-SAT when the underlying graphs belong to an association scheme by means of a certain semidefinite program used to ...
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作者：Kim, Takwon; Yang, Zhou; Jeon, Junkee
作者单位：Sungshin Women's University; South China Normal University; Kyung Hee University
摘要：This paper investigates an optimal consumption, investment, and early retirement problem in the presence of a mandatory retirement date and a borrowing constraint that prohibits borrowing against future labor income during employment. To handle the borrowing constraint, we employ a dual-martingale approach and reformulate the problem as a finite-horizon, two-player, zero-sum game between a singular controller and a stopper. The value of the game is characterized by a parabolic variational ineq...
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作者：Kahale, Nabil
作者单位：heSam Universite; ESCP Business School
摘要：We consider an online least squares regression problem with optimal solution u' and Hessian matrix H, and study a time-average stochastic gradient descent estimator of u'. For k >= 2, we provide an unbiased estimator of u' that is a modification of the timeaverage estimator and runs with an expected number of time-steps of order k, with O(1=k) expected excess risk. The constant behind the O notation depends on parameters of the regression and is a polylogarithmic function of the smallest eigen...
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作者：Hu, Xiaomeng; Klep, Igor; Nie, Tiawang
作者单位：University of California System; University of California San Diego; University of Ljubljana; University of Primorska
摘要：This paper studies Positivstellensatze and moment problems for sets K that are given by universal quantifiers. Let Q be the closed set of universal quantifiers. Fix a finite nonnegative Borel measure whose support is Q and assume it satisfies the multivariate Carleman condition. First, we prove a Positivstellensatz with universal quantifiers: if a polynomialf is positive on K, then f belongs to the associated quadratic module, under the archimedeanness assumption. Second, we prove some necessa...
