EXISTENCE RESULTS FOR GLOBALLY EFFICIENT SOLUTIONS OF VECTOR EQUILIBRIUM PROBLEMS VIA A GENERALIZED KKM PRINCIPLE

The aim of this article is to present new existence results for globally efficient solutions of a strong vector equilibrium problem given by a sum of two functions via a generalized KKM principle, and to establish the connectedness of the solutions set.

Brain networks modeling for studying the mechanism underlying the development of Alzheimer’s disease

Alzheimer’s disease is a primary age-related neurodegenerative disorder that can result in impaired cognitive and memory functions.Although connections between changes in brain networks of Alzheimer’s disease patients have been established,the mechanisms that drive these alterations remain incompletely understood.This study,which was conducted in 2018 at Northeastern University in China,included data from 97 participants of the Alzheimer’s Disease Neuroimaging Initiative(ADNI)dataset covering genetics,imaging,and clinical data.All participants were divided into two groups:normal control(n=52;20 males and 32 females;mean age 73.90±4.72 years)and Alzheimer’s disease(n=45,23 males and 22 females;mean age 74.85±5.66).To uncover the wiring mechanisms that shaped changes in the topology of human brain networks of Alzheimer’s disease patients,we proposed a local naive Bayes brain network model based on graph theory.Our results showed that the proposed model provided an excellent fit to observe networks in all properties examined,including clustering coefficient,modularity,characteristic path length,network efficiency,betweenness,and degree distribution compared with empirical methods.This proposed model simulated the wiring changes in human brain networks between controls and Alzheimer’s disease patients.Our results demonstrate its utility in understanding relationships between brain tissue structure and cognitive or behavioral functions.The ADNI was performed in accordance with the Good Clinical Practice guidelines,US 21 CFR Part 50-Protection of Human Subjects,and Part 56-Institutional Review Boards(IRBs)/Research Good Clinical Practice guidelines Institutional Review Boards(IRBs)/Research Ethics Boards(REBs).

Globally Proper Saddle Point in Ic-Cone-Convexlike Set-Valued Optimization Problems

The existence conditions of globally proper efficient points and a useful property of ic- cone-convexlike set-valued maps are obtained. Under the assumption of the ic-cone-convexlikeness, the optimality conditions for globally proper efficient solutions are established in terms of Lagrange multipliers. The new concept of globally proper saddle-point for an appropriate set-valued Lagrange map is introduced and used to characterize the globally proper efficient solutions. The results which are obtained in this paper are proven under the conditions that the ordering cone need not to have a nonempty interior.

Sequential ensemble optimization based on general surrogate model prediction variance and its application on engine acceleration schedule design

The Efficient Global Optimization(EGO)algorithm has been widely used in the numerical design optimization of engineering systems.However,the need for an uncertainty estimator limits the selection of a surrogate model.In this paper,a Sequential Ensemble Optimization(SEO)algorithm based on the ensemble model is proposed.In the proposed algorithm,there is no limitation on the selection of an individual surrogate model.Specifically,the SEO is built based on the EGO by extending the EGO algorithm so that it can be used in combination with the ensemble model.Also,a new uncertainty estimator for any surrogate model named the General Uncertainty Estimator(GUE)is proposed.The performance of the proposed SEO algorithm is verified by the simulations using ten well-known mathematical functions with varying dimensions.The results show that the proposed SEO algorithm performs better than the traditional EGO algorithm in terms of both the final optimization results and the convergence rate.Further,the proposed algorithm is applied to the global optimization control for turbo-fan engine acceleration schedule design.

Extra Resource Allocation:A DEA Approach in the View of Efficiencies

Data envelopment analysis has been successfully used in resource allocation problems.However,to the best of our knowledge,there are no allocation models proposed in the literature that simultaneously take both the global efficiency and growing potential into account.Hence,this research aims at developing an allocation model for extra input resources,which maximizes the global technical efficiency and scale efficiency of a decision-making unit(DMU)set while maintaining the pure technical efficiency(i.e.,growing potential)of each DMU.To this purpose,we first discuss the optimal resources required by each DMU.We prove that the optimal inputs for the DMU are actually the inputs of some most productive scale size(MPSS).We then propose the allocation model based on the discussion on the case of one DMU.The allocation model is illustrated using two numerical examples.

Painlevé-Kuratowski Stability of the Solution Sets to Perturbed Vector Generalized Systems

In this paper, stability results of solution mappings to perturbed vector generalized system are studied. Firstly, without the assumption of monotonicity, the Painleve-Kuratowski convergence of global efficient solution sets of a family of perturbed problems to the corresponding global efficient solution set of the generalized system is obtained, where the perturbations are performed on both the objective function and the feasible set. Then, the density and Painleve-Kuratowski convergence results of efficient solution sets are established by using gamma convergence, which is weaker than the assumption of continuous convergence. These results extend and improve the recent ones in the literature.

Second-order Optimality Conditions for Cone-subarcwise Connected Set-valued Optimization Problems

The concept of a cone subarcwise connected set-valued map is introduced. Several examples are given to illustrate that the cone subarcwise connected set-valued map is a proper generalization of the cone arcwise connected set-valued map, as well as the arcwise connected set is a proper generalization of the convex set,respectively. Then, by virtue of the generalized second-order contingent epiderivative, second-order necessary optimality conditions are established for a point pair to be a local global proper efficient element of set-valued optimization problems. When objective function is cone subarcwise connected, a second-order sufficient optimality condition is also obtained for a point pair to be a global proper efficient element of set-valued optimization problems.