Feasible Point Research Articles

An Algorithm for Solving Quadratic Programming Problems with an M-matrix

In this study, we propose an approach for solving a quadraticprogramming problem with an M-matrix and simple constraints (QPs). It isbased on the algorithms of Luk-Pagano and Stachurski. These methods usethe fact that an M-matrix possesses a nonnegative inverse which allows tohave a sequence of feasible points monotonically increasing. Introducing theconcept of support for an objective function developed by Gabasov et al., ourapproach leads to a more general condition which allows to have an initialfeasible solution, related to a coordinator support and close to the optimalsolution. The programming under MATLAB of our method and that of Lukand Pagano has allowed us to make a comparison between them, with anillustration on two numerical examples.

Solving Bilevel Programs Based on Lower-Level Mond-Weir Duality

This paper focuses on developing effective algorithms for solving a bilevel program. The most popular approach is to replace the lower-level problem with its Karush-Kuhn-Tucker conditions to generate a mathematical program with complementarity constraints (MPCC). However, MPCC does not satisfy the Mangasarian-Fromovitz constraint qualification (MFCQ) at any feasible point. In this paper, inspired by a recent work using the lower-level Wolfe duality (WDP), we apply the lower-level Mond-Weir duality to present a new reformulation, called MDP, for bilevel program. It is shown that, under mild assumptions, they are equivalent in globally or locally optimal sense. An example is given to show that, different from MPCC, MDP may satisfy the MFCQ at its feasible points. Relations among MDP, WDP, and MPCC are investigated. On this basis, we extend the MDP reformulation to present another new reformulation (called eMDP), which has similar properties to MDP. Furthermore, to compare two new reformulations with the MPCC and WDP approaches, we design a procedure to generate 150 tested problems randomly and comprehensive numerical experiments show that MDP has quite evident advantages over MPCC and WDP in terms of feasibility to the original bilevel programs, success efficiency, and average CPU time, whereas eMDP is far superior to all other three reformulations. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the National Natural Science Foundation of China [Grants 12071280 and 11901380]. 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.2023.0108 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0108 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Mathematical modeling and bifurcation analysis of a delayed eco-epidemiological model with disease in predator and linear harvesting

ABSTRACT This study proposes a three-dimensional prey-predator model with disease in predators, including the time delay due to the gestation of the predator population. The positive invariance of the solutions and the existence of equilibria in the proposed system have been explained. We also analyse the local stability of all feasible equilibrium points for the delayed and non-delayed systems. Additionally, the system’s Hopf bifurcation with regard to several parameters has been investigated. Further, the existence of periodic solutions through Hopf bifurcation is shown with respect to time delay, and it is also shown that time delay is crucial in order to control the dynamics of the system. Explicit formulas are presented to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solution using the normal form theory and the centre manifold theorem. The outcome of the theoretical investigation is ultimately validated through numerical simulation.

DIVERSIFIKASI PENDAPATAN DALAM USAHA PETERNAKAN AYAM PETELUR DI UD MEGA PUTIH LIMBOTO

The research aimed to (1) determine the production process in layer chicken farming at UD Mega Putih and (2) determine the diversification of profits and feasibility of layer chicken farming at UD Mega Putih. This research used descriptive research in the form of a case study. The informants involved in this research were employees at UD Mega Putih, where primary data and secondary data were used in research activities. The data were collected through in-depth interviews and observation while the data analysis was carried out using income analysis, business feasibility, and break-even point. The analysis included cage depreciation cost, equipment depreciation cost, tax cost, seed cost, feed cost, medicine cost, electricity cost, labor cost, and marketing cost in one cycle, namely 2 years (730 days) by calculating based on the results field observation, namely interviewing respondent (Owner of UD Mega Putih). The research findings indicated that the UD Mega Putih layer chicken farming business earned an income of IDR 7,888,166,667/ cycle (730 days) for layer chicken with several 9,500 chickens, IDR 70,000,000/ cycle (60 days) for pullets with several 1000 chickens, and IDR 990,000/ cycle (60 days) for 90 sacks of manure. Thus, the income earned from the layer hen farming business at UD Mega Putih was feasible and profitable.

Development of a multi-leader multi-follower game to design industrial symbioses

The implementation of industrial symbioses all over the world has been proven to be a significant lever to decarbonize production facilities. By enhancing cooperation and exchanging resources, important decrease of emissions can be achieved while reducing operating costs. In the light of our previous work, a game theory model is developed to design resources exchanges in eco-industrial parks (EIP). This new model allows to take into account each authority of an industrial park as an independent player, thus becoming a multi-leader-multi-follower game (MLMFG) model. Water and energy networks are generated simultaneously in the model through a well-known case study. The bi-level model is designed with the water and energy managers as leaders and the plants as followers. In this way, the plants play a Nash game with each other and so do the EIP managers. These managers choose a solution from among the equilibria of the followers before reaching their own equilibrium. The results obtained are then compared with those of the previous article, demonstrating that the MLMFG model provides fairly interesting conclusions for the factories and also for the authorities. The relative gain for the companies is around 30 % for all the factories, which constitutes a strong argument of fairness to convince them to participate in the symbiosis. The result obtained after solving the MLMFG problem is very different from that obtained using the AHP method on the set of feasible solutions. To demonstrate the decision-making aspect of the MLMFG method, the coefficients of the AHP method were identified to find the solution to the MLMFG problem among all the feasible points. It is shown that the coefficients are difficult to determine for an expert, despite the relevance of the solution found.

Optimality conditions and constraint qualifications for cardinality constrained optimization problems

The cardinality constrained optimization problem (CCOP) is an optimization problem where the maximum number of nonzero components of any feasible point is bounded. In this paper, by rewriting the cardinality constraint as a constraint requiring that any feasible point must lie in the union of certain subspaces, we consider CCOP as a mathematical program with disjunctive subspaces constraints (MPDSC). Since a subspace is a special case of a convex polyhedral set, MPDSC is a special case of the mathematical program with disjunctive constraints (MPDC). Using the special structure of subspaces, we are able to obtain more precise formulas for the tangent and (directional) normal cones for the disjunctive set of subspaces. We then obtain first and second order optimality conditions by using the corresponding results from MPDC. Thanks to the special structure of the subspace, we are able to obtain some results for MPDSC that do not hold in general for MPDC. In particular we show that the relaxed constant positive linear dependence (RCPLD) is a sufficient condition for the metric subregularity/error bound property for MPDSC which is not true for MPDC in general. Finally we show that under all constraint qualifications presented in this paper, certain exact penalization holds for CCOP.

On Robust Controlled Invariants for Continuous-time Monotone Systems

This paper delves into the problem of computing robust controlled invariants for monotone continuous-time systems, with a specific focus on lower-closed specifications. We consider the classes of state monotone (SM) and control-state monotone (CSM) systems, we provide the structural properties of robust controlled invariants for these classes of systems and show how these classes significantly impact the computation of invariants. Additionally, we introduce a notion of feasible points, demonstrating that their existence is sufficient to characterize robust controlled invariants for the considered class of systems. The study further investigates the necessity of reducing the feasibility condition for CSM and Lipschitz systems, unveiling conditions that guide this reduction. Leveraging these insights, we construct an algorithm for the computation of robust controlled invariants. To demonstrate the practicality of our approach, we applied the developed algorithm to the coupled tank problem.

Anisotropic structural, vibrational, electronic, optical, and elastic properties of single-layer hafnium pentatelluride: an ab initio study.

Motivated by the highly anisotropic nature of bulk hafnium pentatelluride (HfTe5), the structural, vibrational, electronic, optical, and elastic properties of single-layer two-dimensional (2D) HfTe5 were investigated by performing density functional theory (DFT)-based first-principles calculations. Total energy and geometry optimizations reveal that the 2D single-layer form of HfTe5 exhibits in-plane anisotropy. The phonon band structure shows dynamic stability of the free-standing layer and the predicted Raman spectrum displays seven characteristic Raman-active phonon peaks. In addition to its dynamic stability, HfTe5 is shown to exhibit thermal stability at room temperature, as confirmed by quantum molecular dynamics simulations. Moreover, the obtained elastic stiffness tensor elements indicate the mechanical stability of HfTe5 with its orientation-dependent soft nature. The electronic band structure calculations show the indirect-gap semiconducting behavior of HfTe5 with a narrow electronic band gap energy. The optical properties of HfTe5, in terms of its imaginary dielectric function, absorption coefficient, reflectance, and transmittance, are shown to exhibit strong in-plane anisotropy. Furthermore, structural analysis of several point defects and their oxidized structures was performed by means of simulated STM images. Among the considered vacancy defects, namely , , VTeout, VTein, , and VHf, the formation of VTeout is revealed to be the most favorable defect. While and VHf defects lead to local magnetism, only the oxygen-substituted VHf structure possesses magnetism among the oxidized defects. Moreover, it is found that all the bare and oxidized vacant sites can be distinguished from each other through the STM images. Overall, our study indicates not only the fundamental anisotropic features of single-layer HfTe5, but also shows the signatures of feasible point defects and their oxidized structures, which may be useful for future experiments on 2D HfTe5.

A Stage-structure Leslie-Gower Model with Linear Harvesting and Disease in Predator

The growth dynamics of various species are affected by various aspects. Harvesting interventions and the spread of disease in species are two important aspects that affect population dynamics and it can be studied. In this work, we consider a stage-structure Leslie–Gower model with linear harvesting on the both prey and predator. Additionally, we also consider the infection aspect in the predator population. The population is divided into four subpopulations: immature prey, mature prey, susceptible predator, and infected predator. We analyze the existences and stabilities of feasible equilibrium points. Our results shown that the harvesting in prey and the disease in predator impacts the behavioral of system. The situation in the system is more complex due to disease in the predator population. Some numerical simulations are given to confirm our results.

Cooperative strategy based on a two-layer game model for inferior USVs to intercept a superior USV

Aiming at the problem of inferior USVs intercepting a superior USV, a cooperative interception strategy based on the two-layer game model is studied. Through the mathematical description of the USV's reachable set, the feasible interception point position is obtained. Two necessary conditions for completing regional defensive tasks under nonlinear motion conditions are proposed. By introducing the idea of a hierarchical task network, the complex regional defensive task is divided into different sub-tasks corresponding to the above necessary conditions. In order to better complete the switching between different sub-tasks, a two-layer game model is established. The selection of sub-tasks is modeled as an upper game, and the selection of basic maneuvers is modeled as a lower game. The Monte Carlo simulation results show that the cooperative interception strategy proposed in this paper has better performance under different conditions.

An intuitionistic fuzzy differential equation approach for the lake water and sediment phosphorus model

Intuitionistic fuzzy sets cannot consider the degree of indeterminacy (i.e., the degree of hesitation). This study presents an intuitionistic fuzzy differential equation approach for the lake water and sediment phosphorus model. We examine the proposed model by assuming generalized trapezoidal intuitionistic fuzzy numbers for the initial condition. Feasible equilibrium points, along with their stability criteria, are evaluated. We describe the characteristics of intuitionistic fuzzy solutions and clarify the difference between strong and weak intuitionistic fuzzy solutions. Numerical simulations are performed in MATLAB to validate the model results.

Worst-Case Iteration Bounds for Log Barrier Methods on Problems with Nonconvex Constraints

Interior point methods (IPMs) that handle nonconvex constraints such as IPOPT, KNITRO and LOQO have had enormous practical success. We consider IPMs in the setting where the objective and constraints are thrice differentiable, and have Lipschitz first and second derivatives on the feasible region. We provide an IPM that, starting from a strictly feasible point, finds a μ-approximate Fritz John point by solving [Formula: see text] trust-region subproblems. For IPMs that handle nonlinear constraints, this result represents the first iteration bound with a polynomial dependence on [Formula: see text]. We also show how to use our method to find scaled-KKT points starting from an infeasible solution and improve on existing complexity bounds. Funding: This work was supported by Air Force Office of Scientific Research [9550-23-1-0242]. A significant portion of this work was done at Stanford where O. Hinder was supported by the PACCAR, Inc., Stanford Graduate Fellowship and the Dantzig-Lieberman fellowship.

Simulation and forecasting CTLs response effectualness against global dynamics of SARS-CoV-2/HIV coinfection

Quantifying the dynamical traits and harshness of SARS-CoV-2/HIV coinfection, a modified deterministic seven compartmental mathematical model is framed at cellular level encapsulating the interrelationships between epithelial cells (predominant target cells of COVID-19 infection), CD4+ T cells (target cells of HIV/AIDS infection), SARS-CoV-2 virions, HIV virions and HIV-specific CTL response. As a way to comprehend the kinetics of SARS-CoV-2/HIV coinfection and to provide prediction of model outcomes, the positivity, boundedness and existence conditions of the biologically feasible equilibrium points have been studied. The criteria of local stability and global stability of the coinfection system around the non-negative equilibrium points have been investigated and the analytical results are enhanced numerically. To measure the influence of the model parameters in SARS-CoV-2/HIV transmission dynamics, sensitivity analysis has been performed. Semi-relative sensitivity analysis demonstrates the maximum deviation of the concentration of infected epithelial cells due to changes in the model parameters and states that six parameters are most sensitive. The numerical simulation stipulates that the COVID-19 infection is likely to be died out from a HIV patient body by increasing the apoptosis of infected epithelial cells and that is possible through the proliferation of the CD4+ T cells count of an individual living with HIV via antiretroviral therapy (ART). Additionally, elevated concentration of CD4+ T cells in people living with HIV assists in heightening the CTLs response to combat COVID-19 and other opportunistic infections.

Optimized Packing of 3D Objects Bounded by Spherical and Conical Surfaces

Introduction. Optimizing the packing of arbitrary geometric objects in additive manufacturing opens up new possibilities for increasing the efficiency of additive manufacturing of parts of a complex configuration due to the saving of energy, material and time resources. Additive manufacturing, a cornerstone in fields such as space engineering, medicine, mechanical engineering, and energy, has its efficiency hinging on the optimization of the 3D printing process. Given its widespread application, refining this process is of utmost importance. The purpose of the paper. The paper aims to develop an approach for packing assembled parts of complex geometry in the working area of a 3D printer, while adhering to the standards of 3D printing. Results. For the analytical description of the complex shaped industrial products, a, so called, “composed spherical cone” is used. This generates a family of such objects as spheres, cylinders, spherical cylinders, cones, truncated cones and spherical discs. Using the normalized quasi-phi-function of composed spherical cones, a mathematical model of the problem is presented in the form of a nonlinear programming problem. A solution strategy is developed, encompassing three primary stages: generation of feasible starting points, search of local minima and search of a better local minimum. Numerical examples of packing various industrial products in a 3D printer chamber is provided. 3D-parts are approximated by composed spherical cones with different metric parameters. Conclusions. The conducted numerical simulation confirms the effectiveness of the proposed optimization approach. This study emphasizes the importance of further research and innovation in the field of 3D printing and its optimization, and also demonstrates the potential of using mathematical models to solve practical problems in a production environment. Keywords: packing, assembled spherical cone, mathematical modeling, optimization, additive manufacturing.

Appearance of chaos and bi-stability in a fear induced delayed predator–prey system: A mathematical modeling study

Since many years ago, it has been only a priori assumption that the diversity of ecological demography is largely influenced by the direct interactions of predator and prey species. But over the years, it has also been recognized that an indirect effect can also affect the system more strongly. The effect of fear on prey species is that it restricts physical activities and feeding times of prey thereby reducing interactions with their predators and leading to an intraspecific competition among predators. By these motives, we investigate a delay-induced model inducing fear of predators on the prey population. Existence of feasible steady points, well posedness of the solutions, local & global stability, subcritical & supercritical bifurcation are well presented. The results show that predator fear reduces both prey and predator populations, but does not affect the steady state of the system. As delay increases within a specific range, it changes the dynamics of the system in a stable–unstable–stable sequences. A small delay shifts an unstable interior equilibrium to a predator-free stable equilibrium. The main result of this study is that a large delay produces chaotic dynamics when cost of fear is high and prey birth is low, whereas a small delay creates bi-stable dynamics when cost of fear is low and prey birth is high. Furthermore, by increasing the competitiveness among the predators, the chaos can be completely controlled. We examine that small fear has a greater effect while relatively large fear has less effect. Delay parameter is responsible for appearing stability switch more than once. Extensive numerical simulations are also carried out for various parameters.

Quantum Interior Point Methods for Semidefinite Optimization

We present two quantum interior point methods for semidefinite optimization problems, building on recent advances in quantum linear system algorithms. The first scheme, more similar to a classical solution algorithm, computes an inexact search direction and is not guaranteed to explore only feasible points; the second scheme uses a nullspace representation of the Newton linear system to ensure feasibility even with inexact search directions. The second is a novel scheme that might seem impractical in the classical world, but it is well-suited for a hybrid quantum-classical setting. We show that both schemes converge to an optimal solution of the semidefinite optimization problem under standard assumptions. By comparing the theoretical performance of classical and quantum interior point methods with respect to various input parameters, we show that our second scheme obtains a speedup over classical algorithms in terms of the dimension of the problem n, but has worse dependence on other numerical parameters.

Transition of patients with metabolic bone disease from paediatric to adult healthcare services: current situation and proposals for improvement

BackgroundThere are currently no models for the transition of patients with metabolic bone diseases (MBDs) from paediatric to adult care. The aim of this project was to analyse information on the experience of physicians in the transition of these patients in Spain, and to draw up consensus recommendations with the specialists involved in their treatment and follow-up.MethodsThe project was carried out by a group of experts in MBDs and included a systematic review of the literature for the identification of critical points in the transition process. This was used to develop a questionnaire with a total of 48 questions that would determine the degree of consensus on: (a) the rationale for a transition programme and the optimal time for the patient to start the transition process; (b) transition models and plans; (c) the information that should be specified in the transition plan; and (d) the documentation to be created and the training required. Recommendations and a practical algorithm were developed using the findings. The project was endorsed by eight scientific societies.ResultsA total of 86 physicians from 53 Spanish hospitals participated. Consensus was reached on 45 of the 48 statements. There was no agreement that the age of 12 years was an appropriate and feasible point at which to initiate the transition in patients with MBD, nor that a gradual transition model could reasonably be implemented in their own hospital. According to the participants, the main barriers for successful transition in Spain today are lack of resources and lack of coordination between paediatric and adult units.ConclusionsThe TEAM Project gives an overview of the transition of paediatric MBD patients to adult care in Spain and provides practical recommendations for its implementation.

Feasibility of high-magnesium nickel slag-fly ash as precursor of magnesium phosphate cement and its hydration mechanism

The aim of this study was to investigate the process conditions, hydration reaction products and mechanism of high-magnesium nickel slag (HMNS)-fly ash (FA) as a precursor of magnesium phosphate cement (MPC). The relationships between properties, hydration products, hydration processes, and micromorphology were investigated by engineering properties, XRD, TG-DSC, FT-IR, Raman, and SEM/EDS. The results showed that the optimal process (HMNS/FA = 1.0/0, NH4H2PO4 dosing of 25 wt%, water-cement ratio of 0.26, the maintenance condition is air maintenance, and 200 mesh particle size of raw materials) prepared the cementitious material with 28 d compressive strength of 58.00 MPa and linear expansion rate of only 2.5 %. The hydration process was a multi-stage process, including the dissolution of NH4H2PO4 and pre-treated HMNS (WHMNS), the precipitation of intermediate hydration products and the formation of struvite, and the formation of gelling phases such as -Si-O-P-, -Al-O-P-, and -Si-O-Al-O-P-. Eventually, a high-strength gel-crystal phase structure consisting of gelling phases such as struvite wrapped around unreacted raw materials and struvite crystals was formed. FA was harmful for cementitious material, and impurities and high levels of Ca in FA reacted with phosphate to form hydration products with a loose porous structure (e.g., brushite). The optimal process sample complies with the 52.5R grade of ordinary Portland cement (GB175-2007); its embodied energy was reduced by more than 73.4 % compared to magnesium phosphate cement (MPC), and the corresponding CO2 emission was reduced by more than 74.2 %. Therefore, it has the potential to partially replace MPC from the environmental and feasibility point of view.

A nonlinear programming algorithm for finite element limit analysis using feasible arc searching technique

AbstractThis article presents a nonlinear programming algorithm for finite element limit analysis (FELA) based on feasible arc searching technique (FAST). The proposed algorithm has the potential to significantly reduce the iteration numbers required for convergence, making it a valuable tool for solving complex optimization problems from FELA. The algorithm also introduces several new features to the existing methods, including: (i) a novel method for determining a reasonable updating step length; (ii) the avoidance of solving an additional “phase one problem” for finding an initial feasible point; and (iii) the proposition of an empirical criterion for detecting infeasibility problems. The effectiveness of the proposed approach has been demonstrated through several classic examples derived from geotechnical engineering. The initial two examples show the superior convergence speed of the novel approach compared to existing methods. Additionally, the third example highlights the efficacy of the feasibility detection criterion for problems involving both prescribed and unknown external forces.

Abstract P3071: Targeting Neutrophil Sting And Type I Interferon Activation In Myocardial Ischemia-Reperfusion Injury

Introduction: Inflammation following myocardial ischemia/reperfusion (MI/R) plays a significant role in damaging cardiomyocytes and influencing infarct size, with neutrophils being the most rapid and numerous cells in the post-MI/R heart at 24 hours post reperfusion. Preliminary single-cell RNA sequencing data shows type I interferon (IFN) responding neutrophils are present in the hearts of mice 24 hours post-MI/R. The following study aims to address how the type I IFN responding neutrophil phenotype identified in single-cell RNA sequencing data affects cardiac inflammation in MI/R. We hypothesize that STING and type I IFN activation in neutrophils in the early stages of inflammation can exacerbate inflammation, causing further damage to the heart in MI/R. Methods: Male C57BL/6J mice (10-11 weeks old) underwent 60 minutes of ischemia followed by reperfusion, and were dosed with either vehicle, a STING inhibitor (H151), or an IFNAR1 antibody (ab) at reperfusion and at 24 hours following reperfusion. Cardiac function was assessed two weeks post-reperfusion via echocardiography and tissue samples were collected for histological analysis. Results: Mice treated with IFNAR1 ab showed significant improvement in ejection fraction (44.9% ± 6.8) compared to mice treated with vehicle (31.9% ± 6.2; One-way ANOVA, N=5-6, p<0.05). Additionally, mice treated with IFNAR1 ab showed significant improvements in left ventricular end systolic volume (LVESD) (3.16mm ± 0.52) compared to vehicle treated mice (3.89mm ± 0.40; One-way ANOVA, N=5-6, p<0.05). Mice treated with H151 showed significant improvement in ejection fraction (43.8% ± 7.1) compared to mice treated with vehicle (31.9% ± 6.2; One-way ANOVA, N=5-6, p<0.05). Treatment with H151 or IFNAR1 ab reduced scar size (7.22% ± 3.6; 7.88% ± 3.1%) compared to mice treated with vehicle (9.74% ± 3.7; N=5-6). Conclusion: These data show that targeting the early IFN response in MI/R can improve cardiac function, and provide a basis for studies identifying the effects of the neutrophil specific STING and type I IFN activation following MI/R. If correct, this pathway could be a powerful and clinically feasible point of intervention to improve cardiac recovery after MI/R.