Table of Content

30 September 2021, Volume 9 Issue 3

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Carbon Emissions Abatement (CEA) Allocation Based on Inverse Slack-Based Model (SBM)

Xiao-Yin Hu, Jian-Shu Li, Xiao-Ya Li, Jin-Chuan Cui

2021, 9(3):  475-498.  doi:10.1007/s40305-020-00303-y

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Carbon emissions abatement (CEA) is an important issue that draws attention from both academicians and policymakers. Data envelopment analysis (DEA) has been a popular tool to allocate the CEA, and most previous works are based on radial DEA models. However, as shown in our paper, these models may give biased results due to their ignorance of slackness. To avoid such problems, we propose an allocation model based on the slack-based model and multiple-objective nonlinear programming to find the CEA allocation plan, which can minimize the GDP loss. The property of nonconvexity makes the model difficult to solve. Thus, we construct an approximation algorithm to solve this model with guaranteed error bounds and complexity. In the empirical application, we take regions of china as an illustrative example and find there is a significant region gap in China. Hence, we group the regions into eastern, central, and western, and give the main results, as well as the superiority of our allocation models compared with radial models.

Proximal Methods with Bregman Distances to Solve VIP on Hadamard Manifolds with Null Sectional Curvature

Erik Alex Papa Quiroz, Paulo Roberto Oliveira

2021, 9(3):  499-523.  doi:10.1007/s40305-020-00311-y

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We present an extension of the proximal point method with Bregman distances to solve variational inequality problems (VIP) on Hadamard manifolds with null sectional curvature. Under some natural assumptions, as for example, the existence of solutions of the VIP and the monotonicity of the multivalued vector field, we prove that the sequence of the iterates given by the method converges to a solution of the problem. Furthermore, this convergence is linear or superlinear with respect to the Bregman distance.

Data-driven Stochastic Programming with Distributionally Robust Constraints Under Wasserstein Distance: Asymptotic Properties

Yu Mei, Zhi-Ping Chen, Bing-Bing Ji, Zhu-Jia Xu, Jia Liu

2021, 9(3):  525-542.  doi:10.1007/s40305-020-00313-w

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Distributionally robust optimization is a dominant paradigm for decision-making problems where the distribution of random variables is unknown. We investigate a distributionally robust optimization problem with ambiguities in the objective function and countably infinite constraints. The ambiguity set is defined as a Wasserstein ball centered at the empirical distribution. Based on the concentration inequality of Wasserstein distance, we establish the asymptotic convergence property of the datadriven distributionally robust optimization problem when the sample size goes to infinity. We show that with probability 1, the optimal value and the optimal solution set of the data-driven distributionally robust problem converge to those of the stochastic optimization problem with true distribution. Finally, we provide numerical evidences for the established theoretical results.

Sparse Estimation of High-Dimensional Inverse Covariance Matrices with Explicit Eigenvalue Constraints

Yun-Hai Xiao, Pei-Li Li, Sha Lu

2021, 9(3):  543-568.  doi:10.1007/s40305-021-00351-y

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Firstly, this paper proposes a generalized log-determinant optimization model with the purpose of estimating the high-dimensional sparse inverse covariance matrices. Under the normality assumption, the zero components in the inverse covariance matrices represent the conditional independence between pairs of variables given all the other variables. The generalized model considered in this study, because of the setting of the eigenvalue bounded constraints, covers a large number of existing estimators as special cases. Secondly, rather than directly tracking the challenging optimization problem, this paper uses a couple of alternating direction methods of multipliers (ADMM) to solve its dual model where 5 separable structures are contained. The first implemented algorithm is based on a single Gauss-Seidel iteration, but it does not necessarily converge theoretically. In contrast, the second algorithm employs the symmetric Gauss-Seidel (sGS) based ADMM which is equivalent to the 2-block iterative scheme from the latest sGS decomposition theorem. Finally, we do numerical simulations using the synthetic data and the real data set which show that both algorithms are very effective in estimating high-dimensional sparse inverse covariance matrix.

A New Stochastic Model for Classifying Flexible Measures in Data Envelopment Analysis

Mansour Sharifi, Ghasem Tohidi, Behrouz Daneshian, Farzin Modarres Khiyabani

2021, 9(3):  569-592.  doi:10.1007/s40305-020-00318-5

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The way to deal with flexible data from their stochastic presence point of view as output or input in the evaluation of efficiency of the decision-making units (DMUs) motivates new perspectives in modeling and solving data envelopment analysis (DEA) in the presence of flexible variables. Because the orientation of flexible data is not pre-determined, and because the number of DMUs is fixed and all the DMUs are independent, flexible data can be treated as random variable in terms of both input and output selection. As a result, the selection of flexible variable as input or output for n DMUs can be regarded as binary random variable. Assuming the randomness of choosing flexible data as input or output, we deal with DEA models in the presence of flexible data whose input or output orientation determines a binomial distribution function. This study provides a new insight to classify flexible variable and investigates the input or output status of a variable using a stochastic model. The proposed model obviates the problems caused by the use of the large M number and using its different values in previous models. In addition, it can obtain the most appropriate efficiency value for decision-making units by assigning the chance of choosing the orientation of flexible variable to the model itself. The proposed method is compared with other available methods by employing numerical and empirical examples.

Stable Matchings in the Marriage Model with Indifferences

Noelia Juarez, Jorge Oviedo

2021, 9(3):  593-617.  doi:10.1007/s40305-020-00315-8

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For the marriage model with indifferences, we define an equivalence relation over the stable matching set. We identify a sufficient condition, the closing property, under which we can extend results of the classical model (without indifferences) to the equivalence classes of the stable matching set. This condition allows us to extend the lattice structure over classes of equivalences and the rural hospital theorem.

Novel Global Optimization Algorithm with a Space-Filling Curve and Integral Function

Zhong-Yu Wang, Yong-Jian Yang

2021, 9(3):  619-640.  doi:10.1007/s40305-020-00294-w

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In this study, we consider the global optimization problem in a hypercube. We use a class of series to construct a curve in a hypercube, which can fill the hypercube, and we present an integral function on the curve. Based on the integral function, we propose an algorithm for solving the global optimization problem. Then, we perform a convergence analysis and numerical experiments to demonstrate the effectiveness of the proposed algorithm.

Pricing Decisions in Dual-Channel Closed-Loop Supply Chain Under Retailer's Risk Aversion and Fairness Concerns

Chun-Fa Li, Xue-Qing Guo, Dong-Lei Du

2021, 9(3):  641-657.  doi:10.1007/s40305-020-00324-7

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This paper studies the price decisions in a dual-channel closed-loop supply chain with a risk-averse retailer and a risk-neutral manufacturer by modeling and analyzing three cases:(1) the retailer does not have fairness concerns; (2) the retailer has fairness concerns and the manufacturer considers it; and (3) the retailer has fairness concerns and the manufacturer does not consider it. The effects of risk aversion and fairness concerns on the pricing decisions, profits and demand are examined in differing scenarios.

An Interior-Point Algorithm for Linear Programming with Optimal Selection of Centering Parameter and Step Size

Ya-Guang Yang

2021, 9(3):  659-671.  doi:10.1007/s40305-020-00312-x

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For interior-point algorithms in linear programming, it is well known that the selection of the centering parameter is crucial for proving polynomiality in theory and for efficiency in practice. However, the selection of the centering parameter is usually by heuristics and separated from the selection of the line-search step size. The heuristics are quite different while developing practically efficient algorithms, such as Mehrotra's predictor-corrector (MPC) algorithm, and theoretically efficient algorithms, such as short-step path-following algorithm. This introduces a dilemma that some algorithms with the best-known polynomial bound are least efficient in practice, and some most efficient algorithms may not be convergent in polynomial time. Therefore, in this paper, we propose a systematic way to optimally select the centering parameter and linesearch step size at the same time, and we show that the algorithm based on this strategy has the best-known polynomial bound and may be very efficient in computation for real problems.

On the Stable Gani-Type Attainability Problem Controlled by Promotion at Maximum Entropy

Virtue Uwabomwen Ekhosuehi

2021, 9(3):  673-690.  doi:10.1007/s40305-020-00301-0

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This study considers the attainability problem in one-step for the stable Gani-type model controlled by promotion within the context of maximum entropy. The technique adopted involves formulating the attainability problem as a constrained optimisation problem wherein the objective is to maximise the Shannon entropy rate subject to certain constraints imposed by the attainable configuration and the sub-stochastic transition matrix. The principle of maximum entropy is used to obtain results that are consistent with the exponential representation of transition probabilities for manpower systems.

Necessary Optimality Conditions for Semi-vectorial Bi-level Optimization with Convex Lower Level: Theoretical Results and Applications to the Quadratic Case

Julien Collonge

2021, 9(3):  691-712.  doi:10.1007/s40305-020-00305-w

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This paper explores related aspects to post-Pareto analysis arising from the multicriteria optimization problem. It consists of two main parts. In the first one, we give first-order necessary optimality conditions for a semi-vectorial bi-level optimization problem:the upper level is a scalar optimization problem to be solved by the leader, and the lower level is a multi-objective optimization problem to be solved by several followers acting in a cooperative way (greatest coalition multi-players game). For the lower level, we deal with weakly or properly Pareto (efficient) solutions and we consider the so-called optimistic problem, i.e. when followers choose amongst Pareto solutions one which is the most favourable for the leader. In order to handle reallife applications, in the second part of the paper, we consider the case where each follower objective is expressed in a quadratic form. In this setting, we give explicit first-order necessary optimality conditions. Finally, some computational results are given to illustrate the paper.

The Continuous Knapsack Problem with Capacities

Huynh Duc Quoc, Nguyen Chi Tam, Tran Hoai Ngoc Nhan

2021, 9(3):  713-721.  doi:10.1007/s40305-020-00298-6

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We address a variant of the continuous knapsack problem, where capacities regarding costs of items are given into account. We prove that the problem is NP-complete although the classical continuous knapsack problem is solvable in linear time. For the case that there exists exactly one capacity for all items, we solve the corresponding problem in O(n log n) time, where n is the number of items.