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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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Worst-Case Optimal Covering of Rectangles by Disks
We provide the solution for a fundamental problem of geometric optimization by giving a complete characterization of worst-case optimal disk...
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A Worst-Case Risk Measure by G-VaR
G-VaR, which is a type of worst-case value-at-risk (VaR), is defined as measuring risk incorporating model uncertainty. Compared with most extant...
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Convergence and worst-case complexity of adaptive Riemannian trust-region methods for optimization on manifolds
Trust-region methods have received massive attention in a variety of continuous optimization. They aim to obtain a trial step by minimizing a...
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Worst-case analysis of clique MIPs
The usual integer programming formulation for the maximum clique problem has several undesirable properties, including a weak LP relaxation, a...
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Packing Disks into Disks with Optimal Worst-Case Density
We provide a tight result for a fundamental problem arising from packing disks into a circular container: The critical density of packing disks in a...
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Some methods to derive the priority weights from the best–worst method matrix and weight efficiency test in view of incomplete pairwise comparison matrix
The Best–Worst Method (BWM) has been recently proposed to derive the weights of criteria using two vectors of the pairwise comparison. For BWM, the...
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An elementary approach to tight worst case complexity analysis of gradient based methods
This work presents a novel analysis that allows to achieve tight complexity bounds of gradient-based methods for convex optimization. We start by...
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Cross-Product Ratio Calculation Under Different Sampling Schemes in Clinical Trials—Case Study of the CYP-GUIDES Trial
AbstractRecent advances in clinical trials have produced effective results for the treatment and prevention of diseases. Therefore, there is always a...
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Accuracy Properties of the Normal Approximation for the Estimators of the Ratio of Binomial Proportions
AbstractThis article is devoted to the investigation of the accuracy for normal approximation of the ratio of binomial proportions estimators. The...
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Statistical Inference for the Cross-Product Ratio under Different Sampling Schemes
AbstractThe problem of comparing Bernoulli trial success probabilities comes up in biological and medical research. In this article, we examine how...
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Planning a Defense That Minimizes a Resource Deficit in the Worst-Case Scenario of Supply Network Destruction
AbstractWe consider same model of planning the defense of edges of a supply network. The vertices of the network represent the consumers and the...
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Bregman-Golden Ratio Algorithms for Variational Inequalities
Variational inequalities provide a framework through which many optimisation problems can be solved, in particular, saddle-point problems. In this...
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Halting Time is Predictable for Large Models: A Universality Property and Average-Case Analysis
Average-case analysis computes the complexity of an algorithm averaged over all possible inputs. Compared to worst-case analysis, it is more...
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Robust Omega ratio optimization using regular vines
We study the robust portfolio optimization model for the Omega ratio when the joint ambiguity in the returns distributions is modeled utilizing...
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Polyhedral Coherent Risk Measure and Distributionally Robust Portfolio Optimization
Polyhedral coherent risk measures and their worst-case constructions with respect to the ambiguity set are considered. For the case of the discrete...
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Improving the approximation ratio for capacitated vehicle routing
We devise a new approximation algorithm for capacitated vehicle routing. Our algorithm yields a better approximation ratio for general capacitated...
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Case Studies
While the previous five chapters introduced concepts on importance measures and discussed their potential applications in the real world, few case...
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Approximation Ineffectiveness of a Tour-Untangling Heuristic
We analyze a tour-uncrossing heuristic for the Euclidean Travelling Salesperson Problem, showing that its worst-case approximation ratio is...