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Hierarchically Distributed Optimization with a Flexible and Complexity-Reducing Algorithm
In this paper, the authors consider distributed convex optimization over hierarchical networks. The authors exploit the hierarchical architecture to...
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On the Complexity of the Plantinga–Vegter Algorithm
We introduce tools from numerical analysis and high dimensional probability for precision control and complexity analysis of subdivision-based...
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Classification of Pathologies on Medical Images Using the Algorithm of Random Forest of Optimal-Complexity Trees
The authors propose an approach to the construction of classifiers in the class of Random Forest algorithms. A genetic algorithm is used to determine...
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Algorithms for Cardinality-Constrained Monotone DR-Submodular Maximization with Low Adaptivity and Query Complexity
Submodular maximization is a NP-hard combinatorial optimization problem regularly used in machine learning and data mining with large-scale data...
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Information complexity of mixed-integer convex optimization
We investigate the information complexity of mixed-integer convex optimization under different types of oracles. We establish new lower bounds for...
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Sample complexity analysis for adaptive optimization algorithms with stochastic oracles
Several classical adaptive optimization algorithms, such as line search and trust-region methods, have been recently extended to stochastic settings...
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Worst-case complexity of an SQP method for nonlinear equality constrained stochastic optimization
A worst-case complexity bound is proved for a sequential quadratic optimization (commonly known as SQP) algorithm that has been designed for solving...
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Estimates of Implementation Complexity for Quantum Cryptanalysis of Post-Quantum Lattice-Based Cryptosystems
AbstractDue to the development of quantum computing, there is a need for the development and analysis of cryptosystems resistant to attacks using a...
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Clustering Complexity and an Approximation Algorithm for a Version of the Cluster Editing Problem
In graph clustering problems, one has to partition the vertex set of a given undirected graph into pairwise disjoint subsets (clusters). Vertices of...
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No dimension-free deterministic algorithm computes approximate stationarities of Lipschitzians
We consider the oracle complexity of computing an approximate stationary point of a Lipschitz function. When the function is smooth, it is well known...
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Asymmetry in the complexity of the multi-commodity network pricing problem
The network pricing problem (NPP) is a bilevel problem, where the leader optimizes its revenue by deciding on the prices of certain arcs in a graph,...
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Polynomial worst-case iteration complexity of quasi-Newton primal-dual interior point algorithms for linear programming
Quasi-Newton methods are well known techniques for large-scale numerical optimization. They use an approximation of the Hessian in optimization...
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Higher analogues of discrete topological complexity
In this paper, we introduce the n th discrete topological complexity and study its properties such as its relation with simplicial...
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Algorithm for Sequential Construction of Spanning Minimal Directed Forests
For a weighted digraph, an efficient algorithm is proposed for construction of minimum weight spanning forests with arbitrary number of trees, up to...
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Iterative regularization for low complexity regularizers
Iterative regularization exploits the implicit bias of optimization algorithms to regularize ill-posed problems. Constructing algorithms with such...
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Complexity of a projected Newton-CG method for optimization with bounds
This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity...
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Group actions and higher topological complexity of lens spaces
In this paper, we obtain an upper bound on the higher topological complexity of the total spaces of fibrations. As an application, we improve the...
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On the Computational Complexity of Compressed Power Series
AbstractWe present computational algorithms and complexity estimates for power series in which all exponents are positive integers raised to one and...
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Shortest path with acceleration constraints: complexity and approximation algorithms
We introduce a variant of the Shortest Path Problem (SPP), in which we impose additional constraints on the acceleration over the arcs, and call it...
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Global algorithm for effectively solving min-max affine fractional programs
This article investigates solving the min-max affine fractional programming problem (MAFPP), which arises in systems science and engineering. For...