Minimization Problem Research Articles

Secure transmission of IRS-UAV buffer-aided relaying system with delay constraint

This paper investigates the secure communication between legitimate users in the presence of eavesdroppers, where the Intelligent Reflective Surface-Unmanned Aerial Vehicle (IRS-UAV) and Buffer-Aided (BA) relaying techniques are utilized to enhance secrecy performance. By jointly optimizing the link selection strategy, the UAV position, and the reflection coefficient of the IRS, we aim to maximize the long-term average secrecy rate. Specifically, we propose a novel buffer in/out stabilization scheme based on the Lyapunov framework, which transforms the long-term average secrecy rate maximization problem into two per-slot drift-plus-penalty minimization problems with different link selection factors. The hybrid Particle Swarm Optimization-Artificial Fish Swarm Algorithm (PSO-AFSA) is adopted to optimize the UAV position, and the IRS reflection coefficient optimization problem is solved by iterative optimization in which auxiliary variables and standard convex optimization algorithms are introduced. Finally, the delay constraint is set to ensure the timeliness of information packets. Simulation results demonstrate that our proposed scheme outperforms the comparison schemes in terms of average secrecy rate. Specifically, the addition of BA improves the average secrecy rate by 1.37 bps/Hz, and the continued optimizations of IRS reflection coefficients and UAV positions improve the average secrecy rate by 2.46 bps/Hz and 3.75 bps/Hz, respectively.

A Stable Solution of a Nonuniformly Perturbed Quadratic Minimization Problem by the Extragradient Method with Step Size Separated from Zero

A Stable Solution of a Nonuniformly Perturbed Quadratic Minimization Problem by the Extragradient Method with Step Size Separated from Zero

Physically consistent temperature fields for geophysical inversion based on the parametrized location of an isotherm

PurposeThis paper aims to provide a method for obtaining physically sound temperature fields to be used in geophysical inversions in the presence of immersed essential conditions.Design/methodology/approachThe method produces a thermal field in agreement with a given location of the interface between the Lithosphere and Asthenosphere. It leverages the known location of the interface to enforce the location of a given isotherm while relaxing other constraints known with less precision. The method splits the domain: in the Lithosphere the solution is immediately obtained by standard procedures, while in the Asthenosphere a minimization problem is solved to fulfill continuity of temperatures (strongly imposed) and fluxes at the interface (weakly imposed).FindingsThe numerical methodology, based on the relaxation of the bottom fluxes, correctly recovers the thermal field in the complete domain. To obtain bottom fluxes following geophysical expected values, a constrained minimization strategy is required. The sensitivity of the method could be improved by relaxing other quantities such as lateral fluxes or mantle velocities.Originality/valueA statement of the energy balance problem in terms of a known immersed condition is presented. A novel numerical procedure based on a domain-splitting strategy allows the solution of the problem. The procedure is tailored to be used within geophysical inversions and provides physically sound solutions.

Double Inertial Krasnosel'skii-Mann-Type Method for Approximating Fixed Point of Nonexpansive Mappings

In this paper, we investigate a new method motivated by current advancements in general inertial algorithms. Specifically, we incorporate double inertial extrapolation terms into an iterative sequence, derived from Krasnosel'skii-Mann techniques. The weak convergence theorem for fixed points of nonexpansive mappings in real Hilbert spaces is established. The theoretical developments are rigorously proven, extending existing methods in literature. We also utilize our convergence analysis to solve real-world problems, such as convex minimization problems and zero finding for sums of monotone operators.

Stochastic Gauss-Newton method for estimating absorption and scattering in optical tomography with the Monte Carlo method for light transport.

Image reconstruction in optical tomography in the so-called transport regime, where the diffusion approximation is not valid, requires modeling of light transport using the radiative transfer equation. In this work, we approach this problem by utilizing the Monte Carlo method for light transport. In this work, we propose a methodology for absolute imaging of absorption and scattering in this regime utilizing a Monte Carlo method for light transport. The image reconstruction problem is formulated as a minimization problem that is solved using a stochastic Gauss-Newton method. In the construction of the Jacobian matrix for scattering, a perturbation approximation for Monte Carlo is utilized. The approach is evaluated with numerical simulations using an adaptive approach where the number of photon packets is adjusted during the iterations, and with different fixed numbers of photon packets. The simulations show that the Monte Carlo method for light transport can be utilized in the absolute imaging problem of optical tomography and that the absorption and scattering parameters can be estimated simultaneously with good accuracy.

Synthetic lethality and the minimal genome size problem.

Gene knockout studies suggest that ~300 genes in a bacterial genome and ~1,100 genes in a yeast genome cannot be deleted without loss of viability. These single-gene knockout experiments do not account for negative genetic interactions, when two or more genes can each be deleted without effect, but their joint deletion is lethal. Thus, large-scale single-gene deletion studies underestimate the size of a minimal gene set compatible with cell survival. In yeast Saccharomyces cerevisiae, the viability of all possible deletions of gene pairs (2-tuples), and of some deletions of gene triplets (3-tuples), has been experimentally tested. To estimate the size of a yeast minimal genome from that data, we first established that finding the size of a minimal gene set is equivalent to finding the minimum vertex cover in the lethality (hyper)graph, where the vertices are genes and (hyper)edges connect k-tuples of genes whose joint deletion is lethal. Using the Lovász-Johnson-Chvatal greedy approximation algorithm, we computed the minimum vertex cover of the synthetic-lethal 2-tuples graph to be 1,723 genes. We next simulated the genetic interactions in 3-tuples, extrapolating from the existing triplet sample, and again estimated minimum vertex covers. The size of a minimal gene set in yeast rapidly approaches the size of the entire genome even when considering only synthetic lethalities in k-tuples with small k. In contrast, several studies reported successful experimental reductions of yeast and bacterial genomes by simultaneous deletions of hundreds of genes, without eliciting synthetic lethality. We discuss possible reasons for this apparent contradiction.IMPORTANCEHow can we estimate the smallest number of genes sufficient for a unicellular organism to survive on a rich medium? One approach is to remove genes one at a time and count how many of such deletion strains are unable to grow. However, the single-gene knockout data are insufficient, because joint gene deletions may result in negative genetic interactions, also known as synthetic lethality. We used a technique from graph theory to estimate the size of minimal yeast genome from partial data on synthetic lethality. The number of potential synthetic lethal interactions grows very fast when multiple genes are deleted, revealing a paradoxical contrast with the experimental reductions of yeast genome by ~100 genes, and of bacterial genomes by several hundreds of genes.

Shape optimization for a nonlinear elliptic problem related to thermal insulation

In this paper, we consider a minimization problem of a nonlinear functional I_{\beta,p}(D,\Omega) related to a thermal insulation problem with a convection term, where \Omega is a bounded connected open set in \R^{n} and D\subset\overline{\Omega} is a compact set. The Euler–Lagrange equation relative to I_{\beta,p} is a p -Laplace equation, 1<p<\infty , with a Robin boundary condition with parameter \beta>0 . The main aim is to study extremum problems for I_{\beta,p}(D,\Omega) , among domains D with given geometrical constraints and \Omega\setminus D of fixed thickness. In the planar case, we show that under perimeter constraint the disk maximizes I_{\beta,p} . In the n -dimensional case we restrict our analysis to convex sets showing that the same is true for the ball but under different geometrical constraints.

A distributionally robust approach for the parallel machine scheduling problem with optional machines and job tardiness

This paper investigates a parallel machine scheduling problem with uncertain job processing time, where the job tardiness and optional machines are considered. To address the factor of energy saving, only a subset of all available machines are turned on, which is referred to as not-all-machine (NAM). To depict the uncertain processing time, a mean–mean absolute deviation (MAD) ambiguity set is utilized, and the cost of job tardiness is minimized under the worst-case distribution scenario over the ambiguity set. After building a distributionally robust optimization (DRO) model, theoretical bounds of the optimal number of machines are obtained. Since the model is not computationally scalable, an upper bound on its inner minimization problem is employed, and a mixed integer linear programming (MILP) approximation is obtained based on McCormick inequalities. For the DRO model, tailored speedup techniques are employed, significantly enhancing the computational performance. To evaluate the validity of the proposed DRO model, we compare it with its stochastic programming (SP) counterpart under various parameter settings. Numerical experiments demonstrate that the DRO model exhibits strong performance in the worst-case scenarios. As the problem size increases, the DRO model casts clear advantages over the SP model in terms of computational efficiency and reliability. It is observed that the performance of the DRO model is more stable than that of the nominal sequence, especially with loose due dates. Furthermore, the out-of-sample performance under various decision making preferences shed new lights into the trade-off between energy saving and production efficiency.

Distributed and Multi-Agent Reinforcement Learning Framework for Optimal Electric Vehicle Charging Scheduling

The increasing number of electric vehicles (EVs) necessitates the installation of more charging stations. The challenge of managing these grid-connected charging stations leads to a multi-objective optimal control problem where station profitability, user preferences, grid requirements and stability should be optimized. However, it is challenging to determine the optimal charging/discharging EV schedule, since the controller should exploit fluctuations in the electricity prices, available renewable resources and available stored energy of other vehicles and cope with the uncertainty of EV arrival/departure scheduling. In addition, the growing number of connected vehicles results in a complex state and action vectors, making it difficult for centralized and single-agent controllers to handle the problem. In this paper, we propose a novel Multi-Agent and distributed Reinforcement Learning (MARL) framework that tackles the challenges mentioned above, producing controllers that achieve high performance levels under diverse conditions. In the proposed distributed framework, each charging spot makes its own charging/discharging decisions toward a cumulative cost reduction without sharing any type of private information, such as the arrival/departure time of a vehicle and its state of charge, addressing the problem of cost minimization and user satisfaction. The framework significantly improves the scalability and sample efficiency of the underlying Deep Deterministic Policy Gradient (DDPG) algorithm. Extensive numerical studies and simulations demonstrate the efficacy of the proposed approach compared with Rule-Based Controllers (RBCs) and well-established, state-of-the-art centralized RL (Reinforcement Learning) algorithms, offering performance improvements of up to 25% and 20% in reducing the energy cost and increasing user satisfaction, respectively.

Rapid computation of Hopf bifurcation points of continuous and discrete systems through minimization

For an autonomous nonlinear system, the Hopf bifurcation point along the equilibrium path is a critical feature that indicates whether the values of the parameters change from exhibiting fixed-point behavior to having a periodic orbit. To solve these problems, we developed a method of transforming an eigenvalue problem based on the Jacobian matrix at equilibrium into a minimization problem, enabling the rapid identification of a solution. Specifically, this generalized eigenvalue problem is solved by identifying the vector variable after reducing the number of eigenequations by one in the nonhomogeneous linear system. This can be achieved by normalizing the value of a selected nonzero component of the eigenvector and then moving the column containing this component to the other side of the equation. An appropriate merit function was established in terms of the Euclidean norm of the eigenequation, and this merit function was minimized using the golden section search algorithm to determine the eigenparameters of the bifurcation point. The accuracy of the method for identifying the parameter values and the corresponding imaginary eigenvalues at the Hopf bifurcation points was evaluated for numerous examples for both the continuous and discrete systems. The method was both fast and accurate. Moreover, its stability in the presence of noise was investigated, and the method was robust.

An investigation of stochastic trust-region based algorithms for finite-sum minimization

This work elaborates on the TRust-region-ish (TRish) algorithm, a stochastic optimization method for finite-sum minimization problems proposed by Curtis et al. in [F.E. Curtis, K. Scheinberg, and R. Shi, A stochastic trust region algorithm based on careful step normalization, INFORMS. J. Optim. 1(3) (2019), pp. 200–220; F.E. Curtis and R. Shi, A fully stochastic second-order trust region method, Optim. Methods Softw. 37(3) (2022), pp. 844–877]. A theoretical analysis that complements the results in the literature is presented, and the issue of tuning the involved hyper-parameters is investigated. Our study also focuses on a practical version of the method, which computes the stochastic gradient by means of the inner product test and the orthogonality test proposed by Bollapragada et al. in [R. Bollapragada, R. Byrd, and J. Nocedal, Adaptive sampling strategies for stochastic optimization, SIAM. J. Optim. 28(4) (2018), pp. 3312–3343]. It is shown experimentally that this implementation improves the performance of TRish and reduces its sensitivity to the choice of the hyper-parameters.

Nooses and Nazi swastikas on U.S. campuses: an anti-racist call for a rhetorical reframing of hate symbols as violent technologies

ABSTRACT The terrorizing placement of nooses and Nazi swastikas on U.S. college and university campuses has sustained a climate of fear, trauma, and intimidation. University administration responses often invoke protest from targeted communities over their approach. Examining news reports and university statements between 2010 and 2023, we critique universities’ use of the rhetorical framework of “symbols” (e.g., “heinous symbols of hate,” “racist symbols”). We argue that the “symbolism” framework reflects and reinforces a problem of minimization, if not dismissal, when responding to the impact of these events. Drawing on works by rhetorical studies scholars like Matsuda, Altman, Butler, and Ore, we argue that nooses and swastikas must be understood and treated in relation to their material, violent, spatial, and agential oppressive power and viewed through the relationship between the academic environment of white Christian spaces and anti-Black and anti-Jewish violence and exclusion. Coining the term, “technologies of violence,” we invite a rhetorical shift from hate speech and symbols to acts of violent doing and doing to within the context of historical and contemporary phenomena of systemic racism and antisemitism in academia and society. We offer an anti-racist approach to responding to and studying terroristic objects and acts on campuses.

A discontinuous Galerkin based multiscale method for heterogeneous elastic wave equations

In this paper, we develop a local multiscale model reduction strategy for the elastic wave equation in strongly heterogeneous media, which is achieved by solving the problem in a coarse mesh with multiscale basis functions. We use the interior penalty discontinuous Galerkin (IPDG) to couple the multiscale basis functions that contain important heterogeneous media information. The construction of efficient multiscale basis functions starts with extracting dominant modes of carefully defined spectral problems to represent important media feature, which is followed by solving a constraint energy minimization problem. Then a Petrov-Galerkin projection and systematization onto the coarse grid are applied. As a result, an explicit and energy-conserving scheme is obtained for fast online simulation. The method exhibits both coarse-mesh and spectral convergence as long as one appropriately chooses the oversampling size. We rigorously analyze the stability and convergence of the proposed method. Numerical results are provided to show the performance of the multiscale method and confirm the theoretical results.

Deep image prior and weighted anisotropic-isotropic total variation regularization for solving linear inverse problems

Deep learning, particularly unsupervised techniques, has been widely used to solve linear inverse problems due to its flexibility. A notable unsupervised approach is the deep image prior (DIP), which employs a predetermined deep neural network to regularize inverse problems by imposing constraints on the generated image. This article introduces an optimization technique (DIP-AITV) by combining the DIP with the weighted anisotropic-isotropic total variation (AITV) regularization. Furthermore, we utilize the alternating direction method of multipliers (ADMM), a highly flexible optimization technique, to solve the DIP-AITV minimization problem effectively. To demonstrate the benefits of the proposed DIP-AITV method over the state-of-the-art DIP, DIP-TV, DIP-WTV and CS-DIP, we solve two linear inverse problems, i.e., image denoising and compressed sensing. Computation examples on the MSE and PSNR values show that our method outperforms the existing DIP-based methods in both synthetic and real grayscale and color images.

Finding Codes on Infinite Grids Automatically

We apply automata theory and Karp’s minimum mean weight cycle algorithm to minimum density problems in coding theory. Using this method, we find the new upper bound 53/126 ≈ 0.4206 for the minimum density of an identifying code on the infinite hexagonal grid, down from the previous record of 3/7 ≈ 0.4286.

PPM: A boolean optimizer for data association in multi-view pedestrian detection

To accurately localize occluded people in a crowd is a challenging problem in video surveillance. Existing end-to-end deep multi-camera detectors rely heavily on pre-training with the same multiview datasets used for testing, which compromises their real-world applications. An alternative approach presented here is to project the torso lines of the instance segmentation masks from multiple views to the ground plane and propose pedestrian candidates at the intersection points. The candidate selection process is, for the first time, formulated as a logic minimization problem in Boolean algebra. A probabilistic Petrick’s method (PPM) is proposed to seek the minimum number of candidates to account for all the foreground masks while maximizing the joint occupancy likelihoods in multiple views. Experiments on benchmark video datasets have demonstrated the much improved performance of this approach in comparison with the benchmark deep or non-deep algorithms for multiview pedestrian detection.

M-estimate based diffusion active noise control algorithm over distributed networks and its performance analysis

Multi-channel active noise control (ANC) systems can achieve effective attenuation of low-frequency noise in spatial areas and have been extensively studied. Recent works have focused on the application of multitask diffusion strategies in ANC systems based on wireless acoustic sensor and actuator networks (WASAN), which show the advantages of saving computational burden and enhancing flexibility. However, these works all adopt the mean-square error minimization as the optimization criterion, which leads to severe performance degradation in the presence of impulsive noise interference. Therefore, in this paper, we exploit the M-estimate function and the augmented weight vector of the control filter to formulate a robust minimization problem and propose a distributed augmented diffusion filtered-x least mean M-estimate (DADFxLMM) algorithm for multi-channel ANC systems. The proposed algorithm leverages the M-estimate function to overcome the influence of outliers in the error signal and achieves robustness against impulsive noise, and also eliminates the dependence on the symmetry of the acoustic paths by integrating the augmented weight vectors. Moreover, we replace the score function with the update probability of the weight vector to avoid the need for integration and Price’s theorem, and analyze the mean and mean-square performance of the proposed DADFxLMM algorithm under the contaminated Gaussian (CG) noise model. Simulation results under different system configurations demonstrate that the proposed algorithm outperforms the existing multi-channel ANC algorithms in the presence of impulsive noise interference.

Design optimal neural network based on new LM training algorithm for solving 3D - PDEs

In this article, we design an optimal neural network based on new LM training algorithm. The traditional algorithm of LM required high memory, storage and computational overhead because of it required the updated of Hessian approximations in each iteration. The suggested design implemented to converts the original problem into a minimization problem using feed forward type to solve non-linear 3D - PDEs. Also, optimal design is obtained by computing the parameters of learning with highly precise. Examples are provided to portray the efficiency and applicability of this technique. Comparisons with other designs are also conducted to demonstrate the accuracy of the proposed design.

Differentiable Geodesic Distance for Intrinsic Minimization on Triangle Meshes

Computing intrinsic distances on discrete surfaces is at the heart of many minimization problems in geometry processing and beyond. Solving these problems is extremely challenging as it demands the computation of on-surface distances along with their derivatives. We present a novel approach for intrinsic minimization of distance-based objectives defined on triangle meshes. Using a variational formulation of shortest-path geodesics, we compute first and second-order distance derivatives based on the implicit function theorem, thus opening the door to efficient Newton-type minimization solvers. We demonstrate our differentiable geodesic distance framework on a wide range of examples, including geodesic networks and membranes on surfaces of arbitrary genus, two-way coupling between hosting surface and embedded system, differentiable geodesic Voronoi diagrams, and efficient computation of Karcher means on complex shapes. Our analysis shows that second-order descent methods based on our differentiable geodesics outperform existing first-order and quasi-Newton methods by large margins.

Lifting Directional Fields to Minimal Sections

Directional fields, including unit vector, line, and cross fields, are essential tools in the geometry processing toolkit. The topology of directional fields is characterized by their singularities. While singularities play an important role in downstream applications such as meshing, existing methods for computing directional fields either require them to be specified in advance, ignore them altogether, or treat them as zeros of a relaxed field. While fields are ill-defined at their singularities, the graphs of directional fields with singularities are well-defined surfaces in a circle bundle. By lifting optimization of fields to optimization over their graphs, we can exploit a natural convex relaxation to a minimal section problem over the space of currents in the bundle. This relaxation treats singularities as first-class citizens, expressing the relationship between fields and singularities as an explicit boundary condition. As curvature frustrates finite element discretization of the bundle, we devise a hybrid spectral method for representing and optimizing minimal sections. Our method supports field optimization on both flat and curved domains and enables more precise control over singularity placement.