Maximization Problem Research Articles

On the equivalence between Value-at-Risk- and Expected Shortfall-based risk measures in non-concave optimization

We study a non-concave optimization problem in which an insurance company maximizes the expected utility of the surplus under a risk-based regulatory constraint. The non-concavity does not stem from the utility function, but from non-linear functions related to the terminal wealth characterizing the surplus. For this problem, we consider four different prevalent risk constraints (Expected Shortfall, Expected Discounted Shortfall, Value-at-Risk, and Average Value-at-Risk), and investigate their effects on the optimal solution. Our main contributions are in obtaining an analytical solution under each of the four risk constraints in the form of the optimal terminal wealth. We show that the four risk constraints lead to the same optimal solution, which differs from previous conclusions obtained from the corresponding concave optimization problem under a risk constraint. Compared with the benchmark unconstrained utility maximization problem, all the four risk constraints effectively and equivalently reduce the set of zero terminal wealth, but do not fully eliminate this set, indicating the success and failure of the respective financial regulations.1

Predictive Service Provisioning With Online Learning in Wireless Edge Networks

Mobile Edge Computing (MEC) technology can be implemented at cellular base stations, enabling flexible and configurable provisions of services for mobile users to access. Nevertheless, the conventional solutions mainly focus on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">statical</i> service provisioning, which ignores the dynamic nature of the arriving service requests. In this work, we first conduct comprehensive data-driven observations on over 4 million service requests throughout 9,800 base stations. Our key findings suggest that users' demands intrinsically exhibit spatial and temporal patterns, which inevitably lead to performance degradation in statical service provisioning. Motivated by that, we design and implement MobiEdge, a predictive service provisioning system with online learning in wireless edge networks. We propose a graph embedding learning-based model for representation learning, thus to achieve accurate request prediction at different base stations. Then, based on the prediction of incoming service requests, we study the service provisioning reconfiguration problem, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> , how to jointly optimize service placement and corresponding request scheduling across dual timescales, under constraints of network resources and the total budget. By leveraging the submodular technique, we transform the research issue into a submodular function maximization problem under the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$q$</tex-math></inline-formula> -independence system constraint, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$q$</tex-math></inline-formula> is a positive constant related to the ratio of coefficients in constraint conditions. On this basis, we propose a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1/(1+q)$</tex-math></inline-formula> approximation algorithm with rigorous theoretical analysis on the bounded maximum utility. Extensive trace-driven evaluations are conducted over networks of different scales, and MobiEdge shows remarkable performance enhancements by achieving the accuracy of up to 98% in service prediction and an average utility of 92.9% to the optimal solution in service provisioning.

Desingularization of 2D elliptic free-boundary problem with non-autonomous nonlinearity

In this paper, we consider the existence and limiting behaviour of solutions to a semilinear elliptic equation arising from confined plasma problem in dimension two \[ \begin{cases} -\Delta u=\lambda k(x)f(u) &amp; \text{in}\ D,\\ u= c &amp; \displaystyle\text{on}\ \partial D,\\ \displaystyle - \int_{\partial D} \frac{\partial u}{\partial \nu}\,{\rm d}s=I, \end{cases} \] where $D\subseteq \mathbb {R}^2$ is a smooth bounded domain, $\nu$ is the outward unit normal to the boundary $\partial D$ , $\lambda$ and $I$ are given constants and $c$ is an unknown constant. Under some assumptions on $f$ and $k$ , we prove that there exists a family of solutions concentrating near strict local minimum points of $\Gamma (x)=({1}/{2})h(x,\,x)- ({1}/{8\pi })\ln k(x)$ as $\lambda \to +\infty$ . Here $h(x,\,x)$ is the Robin function of $-\Delta$ in $D$ . The prescribed functions $f$ and $k$ can be very general. The result is proved by regarding $k$ as a $measure$ and using the vorticity method, that is, solving a maximization problem for vorticity and analysing the asymptotic behaviour of maximizers. Existence of solutions concentrating near several points is also obtained.

Social equity in international environmental agreements

AbstractThe aim of this paper is to investigate the problem of designing and building International Environmental Agreements (IEAs) taking into account some normative properties. We consider n asymmetric countries of the world, each one generating a quantity of pollutant emissions from the production of goods and services. We assume that individual emissions yield private benefits and negative externalities affecting all countries. To determine its own level of pollution, each state conducts a cost-benefit analysis. The absence of a supranational entity imposing emissions reduction makes IEAs based on voluntary participation. Examining the standard static non-cooperative game-theoretical model of coalition formation, we discover that the resulting emissions allocations might not be equitable à la Foley. It means that there might exist at least one player preferring to implement some other agent’s strategic plan instead of to play her own strategy. With the goal of studying whether equity, at least among coalesced countries, may be a criterion leading to social improvement, we introduce a new optimization rule. We require that members of an environmental coalition have to solve the maximization problem subject to the constraint imposing that they do not envy each other. Analyzing the particular case of two-player games, we get that, when countries are, in a sense, not too different from each other, our new mechanism endogenously induces social equity. By imposing a suitable total emission cap, the same results extend to all those games where our and standard solutions coexist and are different.

Integrated Sensing, Communication, and Computing for Cost-effective Multimodal Federated Perception

Federated learning (FL) is a prominent paradigm of 6G edge intelligence (EI), which mitigates privacy breaches and high communication pressure caused by conventional centralized model training in the artificial intelligence of things (AIoT). The execution of multimodal federated perception (MFP) services comprises three sub-processes, including sensing-based multimodal data generation, communication-based model transmission, and computing-based model training, ultimately competitive on available underlying multi-domain physical resources such as time, frequency, and computing power. How to reasonably coordinate the multi-domain resources scheduling among sensing, communication, and computing, therefore, is vital to the MFP networks. To address the above issues, this paper explores service-oriented resource management with integrated sensing, communication, and computing (ISCC). Specifically, employing the incentive mechanism of the MFP service market, the resources management problem is defined as a social welfare maximization problem, where the concept of “expanding resources” and “reducing costs” is used to enhance learning performance gain and reduce resource costs. Experimental results demonstrate the effectiveness and robustness of the proposed resource scheduling mechanisms.

Robust Design Optimization of Electric Machines with Isogeometric Analysis

In electric machine design, efficient methods for the optimization of the geometry and associated parameters are essential. Nowadays, it is necessary to address the uncertainty caused by manufacturing or material tolerances. This work presents a robust optimization strategy to address uncertainty in the design of a three-phase, six-pole permanent magnet synchronous motor (PMSM). The geometry is constructed in a two-dimensional framework within MATLAB®, employing isogeometric analysis (IGA) to enable flexible shape optimization. The main contributions of this research are twofold. First, we integrate shape optimization with parameter optimization to enhance the performance of PMSM designs. Second, we use robust optimization, which creates a min–max problem, to ensure that the motor maintains its performance when facing uncertainties. To solve this bilevel problem, we work with the maximal value functions of the lower-level maximization problems and apply a version of Danskin’s theorem for the computation of generalized derivatives. Additionally, the adjoint method is employed to efficiently solve the lower-level problems with gradient-based optimization. The paper concludes by presenting numerical results showcasing the efficacy of the proposed robust optimization framework. The results indicate that the optimized PMSM designs not only perform competitively compared to their non-robust counterparts but also show resilience to operational and manufacturing uncertainties, making them attractive for industrial applications.

On incentivizing resource allocation and task offloading for cooperative edge computing

Cooperative edge computing serves as an effective solution to provide reliable and elastic edge computing services through pooling geographically proximate edge resources and efficiently allocating them to users. The incentive mechanism is critical for realizing cooperative edge computing. In this paper, we propose a virtual machine (VM) or container based resource allocation scheme and two market-based mechanisms to stimulate collaboration among edge servers (ESs). Our first mechanism is a novel two-stage double auction based approach where edge resources are allocated to services/VMs at the first stage and then distributed among ESs at the second stage via a two-sided multi-unit auction. To make it more practical, we use markups to set the ask and bid prices for the participants in the market. Moreover, with the concept of virtual sellers and virtual buyers, we cast the multi-unit auction as single-unit one so that the auction becomes tractable. We further propose a price-based decentralized mechanism in case there is no central authority. With an appropriately constructed objective function, we formulate the resource allocation task as a network utility maximization (NUM) problem and leverage the dual-based decomposition theory for a distributed solution. We theoretically prove that both mechanisms guarantee properties such as budget balance and individual rationality for all ESs. Numerical studies with real-world dataset are presented to demonstrate the superior performance of our mechanisms over baselines.

Finding robust and influential nodes from networks under cascading failures using a memetic algorithm

In the research of complex networks, how to find a set of nodes in the network with the most extensive range in the propagation process, i.e., the Influence Maximization (IM) problem, is one of the focal topics. Existing studies mainly consider the information dissemination process on networks and how to select diffusive nodes efficiently, but little attention has been paid to changes related to the network structure. In reality, networked systems are exposed to uncertain interferences and even destructive sabotages, and cascading failures are one common destruction that can cause networks to collapse even if only a small number of nodes fail. In the case of various complex environmental factors, how to select robust and influential nodes, i.e., the robust influence maximization (RIM) problem, is of great importance in promoting the realistic application of the influence maximization problem. This paper investigates the RIM problem under cascading failures to address the shortcomings in previous studies. Based on existing research, a new performance evaluation metric, RS-cf, is designed to assess the level of robust influence in a numerical form. For solving the seed determination problem, a Memetic algorithm towards the RIM problem under cascading failures, MA-RIMCF, is designed to find nodes with stable information propagation capability guided by RS-cf. Experiments have been conducted on both synthetic and realistic networks to validate the performance of the algorithm. Results indicate that MA-RIMCF can obtain competitive candidates over existing approaches, and seeds with robust and influential abilities are generated to solve diffusion dilemmas.

Splitting algorithms for solving state-dependent maximal monotone inclusion problems

We consider the state-dependent maximal monotone inclusion problem and propose forward-backward splitting algorithms for solving it. Strong convergence of the proposed algorithms is established under suitable conditions. For the special separable case, we present an improved Douglas–Rachford variant that can be easily implemented. Moreover, some accelerated forward-backward splitting algorithms are also presented. Preliminary numerical experiments with comparisons to existing results are presented, illustrating the advantages of our methods.

Energy-efficient UAV communication: A NOMA scheme with resource allocation and trajectory optimization.

This work investigates a downlink nonorthogonal multiple access (NOMA) scheme with unmanned aerial vehicle (UAV) aided wireless communication, where a single UAV was regarded as an air base station (ABS) to communicate with multiple ground users. Considering the constraints of velocity and maneuverability, a UAV energy efficiency (EE) model was proposed via collaborative design resource allocation and trajectory optimization. Based on this, an EE maximization problem was formulated to jointly optimize the transmit power of ground users and the trajectory of the UAV. To obtain the optimal solutions, this nonconvex problem was transformed into an equivalent convex optimization problem on the basis of three user clustering algorithms. After several alternating iterations, our proposed algorithms converged quickly. The simulation results show an enhancement in EE with NOMA because our proposed algorithm is nearly 99.6% superior to other OMA schemes.

Radio resource management for OFDM-based dual-function radar-communication: sum-rate and fairness

AbstractThis paper focuses on radio resource management (RRM) in multi-user dual-function radar communication (DFRC) systems using orthogonal frequency division multiplexing (OFDM) waveforms. We propose two RRM schemes, one from the perspective of sum rate maximization and the other from the perspective of user fairness maximization. These optimization problems are non-convex due to the presence of mixed integer terms, making them difficult to solve. To address these challenges, we have employed a decomposition approach to transform these two complex problems into separate, more readily solvable ones. In addressing the sum rate maximization problem, we initially introduce a heuristic greedy algorithm to obtain a resource allocation scheme that satisfies radar performance requirements. Subsequently, we utilize a cyclic iterative method along with KKT conditions to solve the sum rate maximization problem for communication users. Concerning the fairness maximization problem for communication users, we similarly employ a heuristic greedy algorithm to obtain a resource allocation scheme that meets radar performance constraints. Then utilize the Lagrangian dual method to solve the multi-user fairness maximization problem for communication users. Our experimental results confirm the effectiveness of the proposed algorithms.

Energy-efficient two-way full-duplex relay transmission strategy with SWIPT and direct links

In this paper, we improve networks’ spectral efficiency (SE), extend networks’ lifetime, and maximize networks’ energy efficiency (EE) of two-way full-duplex (FD) relay networks. Firstly, to improve networks’ SE and to extend networks’ lifetime simultaneously, we design a two-way FD relay transmission strategy with simultaneous wireless information and power transfer and direct links (DLs). The designed transmission strategy can complete a bidirectional communication in only one time slot with the exists of DLs and the energy-constrained relay node. With the designed transmission strategy, we further give the characteristics of relay amplification factor, the analysis of the designed transmission strategy, and the EE analysis of traditional half-duplex two-way amplify-and-forward relaying. Secondly, to maximize networks’ EE, we present both the EE maximization problems and analyses of the designed transmission strategy with equal power allocation and optimal power allocation. To solve the EE maximization problems, we further propose the alternating optimal algorithm and give complexity analysis of the algorithm. Simulations show that our designed transmission strategy can improve the SE and EE of the networks.

Aperiodic Two-Dimensional Acoustic Black Holes for Broadband Vibration Attenuation in a Strip

Abstract Purpose Acoustic black holes (ABHs) are promising for vibration control in lightweight structures as proven for one- or two-dimensional periodic arrangements. Here, we explored the effects of spatial disorder and heterogeneous designs of ABHs to broaden an intrinsically limited attenuation bandwidth of periodic counterparts. Method We proposed several strategies to introduce non-periodic arrangements and/or different ABH profiles by solving a maximization problem for the attenuation bandwidth of a plate strip decorated by five ABHs. These strategies allow for finding appropriate dimensions and positions of the ABHs by analyzing a small design subset and are verified experimentally. Results The identified periodic heterogeneous ABHs enable greatly extending the attenuation bandwidth, while disordered identical ABHs allow for increasing the attenuation intensity as compared to the corresponding periodic configurations. The mechanisms underlying the wave attenuation enhancement were clarified by tracing the evolution of the wave transmission and structural vibration modes at each design step. We have found that the broadened wave attenuation attributes to the activation of strongly localized modes at broadband frequencies in aperiodic scenarios. These abundant modes are multi-frequency local resonances in ABHs that are sensitive to both the ABH profile and their spatial arrangement. Conclusion We prove that relaxing the periodicity requirement on multiple two-dimensional ABHs can extend the vibration attenuation to broadband regimes below the ABH characteristic frequency, numerically and experimentally. Aperiodic designs of ABHs thus enlarge the design space by enabling a broadband wave mitigation with attenuation intensity comparable to that of periodic counterparts without increasing the structural mass.

Enhancing Throughput in IoT Networks: The Impact of Active RIS on Wireless Powered Communication Systems

This paper investigates the potential of active reconfigurable intelligent surfaces (RIS) to enhance wireless-powered communication networks (WPCNs), addressing the evolving connectivity needs of the internet of things (IoT). Active RIS, capable of amplifying and reflecting signals, offers a solution to surpass the limitations of passive RIS, such as double-fading attenuation, aiming to significantly improve network throughput and coverage. Our research focuses on exploiting the amplification capabilities of active RIS to boost the overall network sum throughput, engaging in a comprehensive optimization of critical network parameters, including time allocation, reflection coefficients, and phase shift matrices specific to active RIS. The formulated problem is non-convex and highly complex due to the coupling of optimization variables. We employed a successive convex approximation algorithm to solve the throughput maximization problem by converting the non-convex constraints into approximated convex constraints and solving them iteratively. Through extensive simulations, we demonstrate that our active RIS-assisted network substantially outperforms networks facilitated by passive RIS, marking a significant advancement in WPCN performance. These findings underscore the potential of active RIS technology in realizing the full capabilities of IoT connectivity.

Fairness-Aware Competitive Bidding Influence Maximization in Social Networks

Competitive influence maximization (CIM) has been studied for years due to its wide application in many domains. Most current studies primarily focus on the microlevel optimization by designing policies for one competitor to defeat its opponents. Furthermore, current studies ignore the fact that many influential nodes have their own starting prices, which may lead to inefficient budget allocation. In this article, we propose a novel competitive bidding influence maximization (CBIM) problem, where the competitors allocate budgets to bid for the seeds attributed to the platform during multiple bidding rounds. To solve the CBIM problem, we propose a fairness-aware multiagent CBIM (FMCBIM) framework. In this framework, we present a multiagent bidding particle environment (MBE) to model the competitors’ interactions and design a starting price adjustment mechanism to model the dynamic bidding environment. Moreover, we put forward a novel multiagent CBIM (MCBIM) algorithm to optimize competitors’ bidding policies. Extensive experiments on five datasets show that our work has good efficiency and effectiveness.

ToupleGDD: A Fine-Designed Solution of Influence Maximization by Deep Reinforcement Learning

Aiming at selecting a small subset of nodes with maximum influence on networks, the Influence Maximization (IM) problem has been extensively studied. Since it is #P-hard to compute the influence spread given a seed set, the state-of-the-art methods, including heuristic and approximation algorithms, faced with great difficulties such as theoretical guarantee, time efficiency, generalization, etc. This makes it unable to adapt to large-scale networks and more complex applications. On the other side, with the latest achievements of Deep Reinforcement Learning (DRL) in artificial intelligence and other fields, lots of works have been focused on exploiting DRL to solve combinatorial optimization problems. Inspired by this, we propose a novel end-to-end DRL framework, ToupleGDD, to address the IM problem in this paper, which incorporates three coupled graph neural networks for network embedding and double deep Q-networks for parameters learning. Previous efforts to solve IM problem with DRL trained their models on subgraphs of the whole network, and then tested on the whole graph, which makes the performance of their models unstable among different networks. However, our model is trained on several small randomly generated graphs with a small budget, and tested on completely different networks under various large budgets, which can obtain results very close to IMM and better results than OPIM-C on several datasets, and shows strong generalization ability. Finally, we conduct a large number of experiments on synthetic and realistic datasets, and experimental results prove the effectiveness and superiority of our model.

On viscous stratified Darcy–Forchheimer flow in a horizontal porous layer with thermal anisotropy and variable permeability

This study analyzes the effect of anisotropy and the internal heat source in a Darcy–Forchheimer porous layer. It is well known that the variations in viscosity can be attributed to the temperature. Therefore, in the present problem, we consider a linear variation in viscosity with temperature for simplicity. We first derived the linear instability theory and then established global stability using the energy functional approach. In the global stability analysis, we show that working with the L2 norm fails to give a sufficient condition for global stability by exhibiting that the associated maximization problem is unbounded in the underlying stability measure space. Then, we show that a conditional stability bound can be achieved by restricting the internal heat source parameter Q with higher-order norms. The eigenvalue problems obtained in linear and nonlinear theories were integrated numerically. The linear and nonlinear instability thresholds are then compared to identify the potential regions of sub-critical instabilities. It is observed that the system is stabilized when the horizontal component of thermal diffusivity dominates and is unstable when the vertical component of thermal diffusivity dominates. We also found that increasing the variable permeability parameter λ destabilized the system. It is observed that increasing viscosity stabilizes the system, and decreasing viscosity encourages the start of convection. It is also interesting that, in the presence of an internal heat source, the region of subcritical instability increases with increasing viscosity effect but reduces with increasing vertical permeability λ.

Covert performance enhancement in NOMA enabled CoMP network with optimal RIS selection

In this paper, we consider the covert rate maximization problem for the cell edge user in a reconfigurable intelligent surface (RIS) aided downlink non-orthogonal multiple access (NOMA) network with coordinated multipoint (CoMP) transmission in the presence of channel estimation errors. We derive the analytical expression for the detection error probability (DEP) at the adversary (Willie) assuming the worst case scenario where they employ optimal detection threshold. With the derived analytical expression, we propose an optimal RIS selection scheme to boost the covert rate. To further improve the covert performance, we optimize the NOMA power allocation coefficients and phase shifts of the selected RIS subject to the target rate and covertness constraints. Simulation results demonstrate the improvement in covert rate and robustness offered by the proposed scheme in the presence of channel estimation errors over other benchmarks.

Формирование оптимального кредитного портфеля с использованием нечётко-множественного подхода

The problem of profit maximization from lending to a financial organization is considered. A set of loan con-tracts forms a loan portfolio, which makes it possible to use the portfolio theory in the study of the designated problem. We will consider the formation of a loan portfolio as the formation of an investment portfolio. The problem arises of redistributing the funds of the investment portfolio in order to minimize its possible risk and maximize profitability. This problem in classical formulation can be solved according to Markowitz risk diversification. Thus, the problem of risk minimization and profitability maximization from lending to a financial institu-tion can be represented as a fuzzy mathematical programming problem, and more specifically, as a fuzzy linear programming problem. The resulting problem is solved by considering discrete α-levels and is reduced to a set of linear programming problems constructed for each of them. A clear expected optimal solution can be obtained by applying the defuzzification method, which allows you to convert a fuzzy set into a crisp number.

The Impact of Passive Social Media Viewers in Influence Maximization

A frequently studied problem in the context of digital marketing for online social networks is the influence maximization problem that seeks for an initial seed set of influencers to trigger an information propagation cascade (in terms of active message forwarders) of expected maximum impact. Previously studied problems typically neglect that the probability that individuals passively view content without forwarding it is much higher than the probability that they forward content. Considering passive viewing enables us to maximize more natural (social media) marketing metrics, including (a) the expected organic reach, (b) the expected number of total impressions, or (c) the expected patronage, all of which are investigated in this paper for the first time in the context of influence maximization. We propose mathematical models to maximize these objectives, whereby the model for variant (c) includes individual’s resistances and uses a multinomial logit model to model customer behavior. We also show that these models can be easily adapted to a competitive setting in which the seed set of a competitor is known. In a computational study based on network graphs from Twitter (now X) and from the literature, we show that one can increase the expected patronage, organic reach, and number of total impressions by 36% on average (and up to 13 times in particular cases) compared with seed sets obtained from the classical maximization of message-forwarding users. History: Accepted by Andrea Lodi, Area Editor for Design &amp; Analysis of Algorithms—Discrete. Funding: This work was supported by the Federal Ministry of Education, Science and Research of Austria and by the Austrian Agency for International Mobility and Cooperation in Education, Science and Research [Reference ICM-2019-13384]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0047 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0047 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .