Search Results (23)

Background: Some widely used wildland fire behavior models, like the Fire Area Simulator (FARSITE), propagate fire fronts by computing the front-normal velocity (spread rate) as a function of local inputs and the front-normal direction. Such models are sometimes observed to cause the collapse of crown fires into sharp wedge shapes that eliminate heading fire behavior. Aims: We set out to document this phenomenon and, more generally, understand the relationships between fire shapes and spread rate functions. Methods: The phenomenon is studied both mathematically and through simulation experiments. Non-smooth fire fronts are theorized mathematically by an Eikonal partial differential equation ($H(x,\tau ,D\tau )=1$), where the unknown $\tau \left(x\right)$ is the time-of-arrival function and the Hamiltonian $H(x,t,p)$ is positively homogeneous and possibly non-convex in p; convex analysis is used to study viscosity solutions in constant conditions. Results: We show that a fire spread model preserves the smoothness of fire fronts if and only if it is equivalent to using the Huygens principle. Nontrivially, this is equivalent to a convexity criterion on the inverse spread rate profile, which is then the polar dual of the Huygens wavelet; this corresponds to Hamiltonian–Lagrangian duality. The relevance of smoothness-destroying models to crown fire is debated. Exact analytical formulas are derived for fire growth in constant conditions. Conclusions: Our understanding of fire spread models is improved by solving the spread equations in more general ways than previously known. In particular, the collapse of heading crown fires into sharp shapes is now explained. Smoothness-destroying spread models cannot be simulated by algorithms based on travel time like cellular automata; their general well-definedness remains an open question. Fire modelers can use these findings to guide their search for improved crown fire models, and more generally to verify the accuracy of numerical implementations. Full article

Support vector regression (SVR) is a well-established kernel-based method for nonlinear regression. However, standard SVR formulations minimize absolute-error losses, which are not consistent with the scale-free, relative-accuracy criteria prevalent in forecasting and industrial applications, where uncertainty is typically expressed as a percentage. This study proposes a unified SVR framework that incorporates percentage-error loss functions and symmetry constraints. Four specific variants are introduced: $\epsilon$-SVR with mean absolute percentage error (MAPE), its symmetric kernel extension, least-squares SVR (LS-SVR) with root mean square percentage error (RMSPE), and its symmetric counterpart. Each variant is formulated in primal, Lagrangian, and dual forms using Karush–Kuhn–Tucker analysis. The principal structural finding is that percentage scaling results in sample-dependent box constraints for $\epsilon$-SVR and a target-weighted diagonal regularization matrix for LS-SVR. In contrast, symmetry modifies only the kernel matrix, leaving the optimization structure unchanged. Convexity and the representer theorem are preserved in all cases. Experiments are conducted on three cross-sectional datasets (Boston Housing, Diabetes, and Energy Efficiency) and a time-series dataset on Victorian electricity demand. Evaluation utilizes three metrics (MAPE, MASE, and MAAPE), 95% bootstrap confidence intervals, and paired Wilcoxon tests, and compares performance against percentage-error-native baselines (weighted-MAE, quantile regression, and log-target SVR), classical $\epsilon$-SVR, Random Forest, and XGBoost. An additional reflection-based experiment assesses the symmetric-kernel variants. The results demonstrate that optimizing for percentage error consistently improves the targeted metric without adversely affecting absolute-error metrics. Full article

Typhoon-induced extreme weather poses a severe threat to power systems with high offshore wind penetration. Source-side wind turbine tripping and grid-side transmission line failures are likely to occur simultaneously, which may trigger cascading outages and large-scale load shedding. A multi-level source-grid-load-storage preventive resilience dispatch strategy is proposed. A typhoon spatiotemporal evolution model is first established based on the Batts gradient wind model. Failure probability models for offshore wind turbines and overhead transmission lines are developed while considering strong wind and lightning strike effects. The most probable and severe fault scenario is identified using an entropy-based quantification method. A two-stage robust preventive dispatch model is subsequently formulated. In the day-ahead stage, unit commitment, multi-type reserve allocation, and pumped storage scheduling are optimized at a 1 h resolution. In the real-time stage, combined wind-storage systems are coordinated at a 10 min resolution to accommodate rapid wind power ramps caused by high-wind shutdown events. The model is reformulated through Lagrangian duality and solved by the Benders decomposition algorithm. Case studies on a modified IEEE-RTS 24-bus system with three offshore wind farms demonstrate that the proposed strategy reduces wind curtailment by 66.3%, load shedding by 74.6%, and total cost by 14.8% compared with the case without energy storage. The combined operation cost of storage resources accounts for only 3.1% of the total cost, confirming its favorable cost-effectiveness for resilience enhancement. The proposed strategy contributes to the sustainable integration of offshore wind energy by ensuring a reliable power supply during extreme weather events. Full article

This paper studies long-term resource allocation for rate-splitting multiple access (RSMA) in multi-carrier downlink systems. RSMA provides a flexible interference-management mechanism that bridges spatial division multiple access (SDMA) and non-orthogonal multiple access (NOMA), but guaranteeing long-term quality-of-service (QoS) performance under dynamic fading channels remains challenging. To address this limitation, we develop an opportunistic scheduling framework based on Lagrangian duality and stochastic optimization, which maximizes the long-term weighted sum rate (WSR) while satisfying per-user time-average QoS constraints. The proposed method decomposes the long-term problem into per-slot subproblems with adaptive effective weights, and each subproblem is efficiently solved through a two-stage procedure consisting of subcarrier–user pair matching and power allocation. Simulation results show that the proposed RSMA scheduling framework significantly outperforms conventional NOMA while ensuring the QoS requirements of all users. These results demonstrate the practical applicability of RSMA for next-generation wireless networks requiring both high spectral efficiency and long-term reliability. Full article

Over-the-air federated learning (Air-FL) has emerged as a promising paradigm that integrates communication and learning, which offers significant potential to enhance model training efficiency and optimize communication resource utilization. This paper addresses the challenge of interference management in multi-cell Air-FL systems, focusing on parallel multi-task scenarios where each cell independently executes distinct training tasks. We begin by analyzing the impact of aggregation errors on local model performance within each cell, aiming to minimize the cumulative optimality gap across all cells. To this end, we formulate an optimization framework that jointly optimizes device transmit power and denoising factors. Leveraging the Pareto boundary theory, we design a centralized optimization scheme that characterizes the trade-offs in system performance. Building upon this, we propose a distributed power control optimization scheme based on interference temperature (IT). This approach decomposes the globally coupled problem into locally solvable subproblems, thereby enabling each cell to adjust its transmit power independently using only local channel state information (CSI). To tackle the non-convexity inherent in these subproblems, we first transform them into convex problems and then develop an analytical solution framework grounded in Lagrangian duality theory. Coupled with a dynamic IT update mechanism, our method iteratively approximates the Pareto optimal boundary. The simulation results demonstrate that the proposed scheme outperforms baseline methods in terms of training convergence speed, cross-cell performance balance, and test accuracy. Moreover, it achieves stable convergence within a limited number of iterations, which validates its practicality and effectiveness in multi-task edge intelligence systems. Full article

This article deals with a class of nonsmooth interval-valued multiobjective semi-infinite programming problems with vanishing constraints (NIMSIPVC). We introduce the VC-Abadie constraint qualification (VC-ACQ) for NIMSIPVC and employ it to establish Karush–Kuhn–Tucker (KKT)-type necessary optimality conditions for the considered problem. Regarding NIMSIPVC, we formulate interval-valued weak vector, as well as interval-valued vector Lagrange-type dual and scalarized Lagrange-type dual problems. Subsequently, we establish the weak, strong, and converse duality results relating the primal problem NIMSIPVC and the corresponding dual problems. Moreover, we introduce the notion of saddle points for the interval-valued vector Lagrangian and scalarized Lagrangian of NIMSIPVC. Furthermore, we derive the saddle-point optimality criteria for NIMSIPVC by establishing the relationships between the solutions of NIMSIPVC and the saddle points of the corresponding Lagrangians of NIMSIPVC, under convexity assumptions. Non-trivial illustrative examples are provided to demonstrate the validity of the established results. The results presented in this paper extend the corresponding results derived in the existing literature from smooth to nonsmooth optimization problems, and we further generalize them for interval-valued multiobjective semi-infinite programming problems with vanishing constraints. Full article

This paper considers a risk-averse Markov decision process (MDP) with non-risk constraints as a dynamic optimization framework to ensure robustness against unfavorable outcomes in high-stakes sequential decision-making situations such as disaster response. In this regard, strong duality is proved while making no assumptions on the problem’s convexity. This is necessary for some real-world issues, e.g., in the case of deprivation costs in the context of disaster relief, where convexity cannot be ensured. Our theoretical results imply that the problem can be exactly solved in a dual domain where it becomes convex. Based on our duality results, an augmented Lagrangian-based constraint handling mechanism is also developed for risk-averse reinforcement learning algorithms. The mechanism is proved to be theoretically convergent. Finally, we have also empirically established the convergence of the mechanism using a multi-stage disaster response relief allocation problem while using a fixed negative reward scheme as a benchmark. Full article

In the future, a high proportion of distributed generations (DG) will be integrated into the distribution network. The existing active distribution network (ADN) planning methods have not fully considered multiple uncertainties, differentiated regulation modes or the cost of multiple types of interconnection switches. Meanwhile, it is difficult to solve large-scale problems at small granularity. Therefore, an expansion planning method of ADN considering the selection of multiple types of interconnection switches is proposed. Firstly, a probability distribution ambiguity set of DG output and electrical-load consumption based on the Wasserstein distance is established for dealing with the issue of source-load uncertainty. Secondly, a distributionally robust optimization model for collaborative planning of distribution network lines and multiple types of switches based on the previously mentioned ambiguity set is established. Then, the original model is transformed into a mixed integer second-order cone programming (SOCP) model by using the convex relaxation method, the Lagrangian duality method and the McCormick relaxation method. Finally, the effectiveness of the proposed method is systematically verified using the example of Portugal 54. The results indicate that the proposed method raises the annual net profit by nearly 5% compared with the traditional planning scheme and improves the reliability and low-carbon nature of the planning scheme. Full article

This paper focuses on the dynamic economic emission dispatch (DEED) problem, to coordinate the distributed energy resources (DERs) in a power system and achieve economical and environmental operation. Distributed energy storages (ESs) are introduced into problem formulation in which charging/discharging efficiency is taken into account. By relaxing the nonconvexity induced by the charging/discharging model of ESs and network losses, we convert the non-convex DEED problem into its convex equivalency. Then, through a Lagrangian duality reformulation, an equivalent unconstrained consensus optimization model is established—a novel consensus-based decentralized algorithm, where the incremental cost is chosen as the consensus variable. At each iteration, only one primal variable requires sub-optimization, and it is completely locally updated. This is different from the well-known alternating direction method of multiplier (ADMM)-based algorithms where more than one subproblem needs to be solved at each iteration. The results of the comparative experiments also reflect the algorithm’s advantage in terms of computational efficiency. The simulation results validate the effectiveness of the proposed algorithm, achieving a balance between emissions and economic considerations. Full article

Mobile edge computing (MEC) powered by unmanned aerial vehicles (UAVs), with the advantages of flexible deployment and wide coverage, is a promising technology to solve computationally intensive communication problems. In this paper, an orthogonal time frequency space (OTFS)-based UAV-assisted MEC system is studied, in which OTFS technology is used to mitigate the Doppler effect in UAV high-speed mobile communication. The weighted total energy consumption of the system is minimized by jointly optimizing the time division, CPU frequency allocation, transmit power allocation and flight trajectory while considering Doppler compensation. Thus, the resultant problem is a challenging nonconvex problem. We propose a joint algorithm that combines the benefits of the atomic orbital search (AOS) algorithm and convex optimization. Firstly, an improved AOS algorithm is proposed to swiftly obtain the time slot allocation and high-quality solution of the UAV optimal path. Secondly, the optimal solution for the CPU frequency and transmit power allocation is found by using Lagrangian duality and the first-order Taylor formula. Finally, the optimal solution of the original problem is iteratively obtained. The simulation results show that the weighted total energy consumption of the OTFS-based system decreases by 13.6% compared with the orthogonal frequency division multiplexing (OFDM)-based system. The weighted total energy consumption of the proposed algorithm decreases by 11.7% and 26.7% compared with convex optimization and heuristic algorithms, respectively. Full article

We demonstrate that the celebrated Stückelberg formalism is modified in the case of a massive four (3 + 1)-dimensional (4D) Abelian 2-form theory due to the presence of a self-duality discrete symmetry in the theory. The latter symmetry entails upon the modified 4D massive Abelian 2-form gauge theory to become a massive model of Hodge theory within the framework of Becchi–Rouet–Stora–Tyutin (BRST) formalism where there is the existence of a set of (anti-)co-BRST transformations corresponding to the usual nilpotent (anti-)BRST transformations. The latter exist in any arbitrary dimension of spacetime for the usual Stückelberg-modified massive Abelian 2-form gauge theory. The modification in the Stückelberg technique is backed by the precise mathematical arguments from the differential geometry where the exterior derivative and Hodge duality operator play the decisive roles. The modified version of the Stückelberg technique remains invariant under the discrete duality transformations which also establish a precise and deep connection between the off-shell nilpotent (anti-)BRST and (anti-)co-BRST transformations. We have clarified a simple trick of using the equations of motion to remove the higher derivative terms in the appropriate Lagrangian densities so that our 4D theory can become consistent. Full article

In this paper, we establish various results of duality for a new class of constrained robust nonlinear optimization problems. For this new class of problems, involving functionals of (path-independent) curvilinear integral type and mixed constraints governed by partial derivatives of second order and uncertain data, we formulate and study Wolfe, Mond-Weir and mixed type robust dual optimization problems. In this regard, by considering the concept of convex curvilinear integral vector functional, determined by controlled second-order Lagrangians including uncertain data, and the notion of robust weak efficient solution associated with the considered problem, we create a new mathematical context to state and prove the duality theorems. Furthermore, an illustrative application is presented. Full article

At present, the power system has the characteristics of mutual independence but interconnection, and the interconnection between the various subsystems brings certain challenges to the distributed computing of the power grid. In addition, a substantial amount of naturally uncertain renewable resources are incorporated into the power system, which will impose volatile dynamics on the grid. In this paper, an alternating direction multiplier method (ADMM) is proposed for the power system with real-time renewables to tackle the online optimal power flow (OPF) problem. Due to the adoption of the Lagrangian duality, the proposed distributed ADMM scheme utilizes consensus ADMM to solve the dual OPF problem, which only discloses boundary coupling via the Lagrangian multiplier and further reduces the amount of information communication. Given the natural uncertainty of distributed energy resources (DER), the algorithm avoids the double-loop implementation or the uncertainty of traditional distributed methods of using the boundary information as equality constraints caused by dynamic DER. It is thus capable of providing a provable performance guarantee and is inherently developed to cope with the dynamic OPF problem with renewables in an online fashion. Taking the IEEE 30-bus system as a test feeder, the simulation results verify the efficiency and robustness of the proposed algorithms in solving both the static and dynamic OPF problems; in addition, the online method can effectively avoid the violent fluctuations of the conventional generator output copying with renewables rapid variation in comparison with the offline algorithms. Full article

We apply the notion of polar duality from convex geometry to the study of quantum covariance ellipsoids in symplectic phase space. We consider in particular the case of “quantum blobs” introduced in previous work; quantum blobs are the smallest symplectic invariant regions of the phase space compatible with the uncertainty principle in its strong Robertson–Schrödinger form. We show that these phase space units can be characterized by a simple condition of reflexivity using polar duality, thus improving previous results. We apply these geometric constructions to the characterization of pure Gaussian states in terms of partial information on the covariance ellipsoid, which allows us to formulate statements related to symplectic tomography. Full article

In the Industrial Internet of Things (IIoT), non-orthogonal multiple access (NOMA) has emerged as a viable multiple access method due to its superior efficiency. In this paper, a new power allocation technique for NOMA-enabled IIoT devices is presented with trade-offs between increasing energy efficiency and decreasing power consumption. We present a joint optimization of transmission rate and energy harvesting in simultaneous wireless information and power transfer (SWIPT) NOMA-enabled IIoT devices. With the power splitting (PS) approach, we examine how to improve overall transmission rate and harvested energy, simultaneously, while fulfilling the minimum rate and harvested energy needs of each IIoT device in a SWIPT-enabled NOMA system. An objective function is established by adding transmission rates obtained from information decoding and the transformed throughput from energy harvesting. The combination of management approaches with Industry 4.0 technology provides a viable strategy to decrease industrial production’s energy use. Several performance metrics may be utilized to study manufacturing process optimization. The efficiency of production equipment may be measured by looking at the overall effectiveness (OE) of the equipment in use. We divide the non-convex optimization problem into two sub-problems, based on the Lagrangian duality method, and solve them to find the optimal solution for the non-convex problem. The approach is validated based on physical layer parameter settings that represent potential factory of the future scenarios. Simulation results confirm the effectiveness of the presented method in a SWIPT-enabled NOMA system, provide considerable performance gains over the classic rate maximization strategy, and demonstrate the energy efficiency of the presented method compared with the conventional system. The results show huge potential of our solutions to reduce the future huge energy demand related to factory automation. Full article