This letter proposes a multi-agent distributed solution for linear programming (LP) problems with time-invariant box constraints on the decision variables and possibly time-varying inequality constraints. This class o...
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This letter proposes a multi-agent distributed solution for linear programming (LP) problems with time-invariant box constraints on the decision variables and possibly time-varying inequality constraints. This class of LP problems is relevant in different multi-agent smart systems. In the proposed approach, each agent computes only a single or a few of decision variables, while convergence to the optimal solution for the overall problem is guaranteed. Using a strong convexification of the problem combined with the barrier method, we prove that, despite the fact that the inequalities are time-varying, the tracking error remains bounded, and the bound is proportional to the rate of change of parameters. The effectiveness of the proposed scheme is demonstrated through a simulation study on a wireless power transfer network.
The present paper is devoted to the computation of the Lipschitz modulus of the optimal value function restricted to its domain in linear programming under different types of perturbations. In the first stage, we stud...
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The present paper is devoted to the computation of the Lipschitz modulus of the optimal value function restricted to its domain in linear programming under different types of perturbations. In the first stage, we study separately perturbations of the right-hand side of the constraints and perturbations of the coefficients of the objective function. Secondly, we deal with canonical perturbations, i.e., right-hand side perturbations together with linear perturbations of the objective. We advance that an exact formula for the Lipschitz modulus in the context of right-hand side perturbations is provided, and lower and upper estimates for the corresponding moduli are also established in the other two perturbation frameworks. In both cases, the corresponding upper estimates are shown to provide the exact moduli when the nominal (original) optimal set is bounded. A key strategy here consists in taking advantage of the background on calmness in linear programming and providing the aimed Lipschitz modulus through the computation of a uniform calmness constant.
Background: The respective roles of plant- and animal-sourced foods in sustainable healthy diets for humans remain unclear. Nutritional quality and the monetary cost of diets are key criteria among others for sustaina...
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Background: The respective roles of plant- and animal-sourced foods in sustainable healthy diets for humans remain unclear. Nutritional quality and the monetary cost of diets are key criteria among others for sustainable food production. Objective: linear programming (LP) was used to determine the composition of nutritionally adequate dietary patterns formulated at the lowest cost. The hypothesis tested was that animal-sourced foods would be included in least-cost diets due to their high density of particular essential nutrients. Methods: The LP modeling work was based on eating patterns, retail food prices (2020), and the daily energy (11,150 kJ, 2665 kcal) and essential nutrient requirements (29 nutrients in total) of a reference adult in New Zealand (NZ). The LP modeling approach is publicly and freely available to readily illustrate the change in dietary profiles and daily diet cost, in the simulation of changes in energy and nutrient requirements, and price fluctuations within food groups. Results: A nutrient-adequate, least-cost dietary pattern formulated from 883 foods, with a daily cost of NZ $3.23, included both animal- and plant-based foods. The nutrients found to be equally first-limiting were biotin, calcium, molybdenum, potassium, selenium, vitamin A, pantothenic acid, and vitamin C. When a dietary scenario with no animal-sourced foods was modeled, by increasing the retail prices of animal-sourced foods by 1.05 to 10.3 times, the daily cost of this plant-only dietary pattern was NZ $4.34. Additional nutrients, such as zinc, vitamin B-12, and vitamin D, were met at their daily minimum required levels. Conclusions: Dietary patterns formulated at the lowest cost and meeting the daily minimum requirements for energy and essential nutrients for an adult in New Zealand relied on foods sourced from animals and plants.
Renewable energy-based electricity is an imperative need for sustainable development. If some other utility outputs can be generated along with electricity then the levelized cost of electricity decreases due to bette...
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Renewable energy-based electricity is an imperative need for sustainable development. If some other utility outputs can be generated along with electricity then the levelized cost of electricity decreases due to better resource utilization. Solar, biomass and wind resources are the inputs to the considered polygeneration system. The outputs of this polygeneration system are electricity, ethanol and chill. Application of proper optimization algorithm is necessary for the proper design of the polygeneration systems. The optimization is carried out using linear programming method to determine the optimum size of the various components. The reliability of power supply and availability of the local resources are the constraints. The minimization of levelized cost of electricity is the objective function. The results of the study show that the levelized cost of electricity for this system in the present area of study is 0.1081 USD/kWh. The sensitivity analysis is carried out to assess the suitability of the system in varying price environment. This study is carried out for a village located in Sunderban deltaic region in the state of West Bengal, India.
Objective We analysed optimal nutrient levels using linear programming (LP) to reveal nutritional shortcomings of Korean dine-out meals and to stress the importance of fruits and dairy products for maintaining a healt...
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Objective We analysed optimal nutrient levels using linear programming (LP) to reveal nutritional shortcomings of Korean dine-out meals and to stress the importance of fruits and dairy products for maintaining a healthy diet. Design LP models that minimize deviation from recommended nutrient values were formulated to analyse deficiency or excess of nutrients under the best situation. Setting Korean dine-out menus and nutritional information were taken from the nutrient composition tables for dine-out menus developed by the Ministry of Food and Drug Safety and the nutrient database from Computerized Analysis Program. Acceptable macronutrient distribution ranges of macronutrients such as carbohydrate, protein and fat, and recommended intake levels for energy, vitamins, minerals and cholesterol, by sex, were based on the Dietary Reference Intake for Koreans aged 30-49 years. Participants Optimization was performed on selecting the optimal Korean meal combination. Results LP optimization models showed that it is unlikely to satisfy all nutrient recommendations with any combination of dine-out menus. Specifically, meal combinations of Korean dine-out menus had high levels of Na and cholesterol and low levels of vitamins and minerals. Four formulations were considered to compare the effects of controlling Na and including fruit and dairy products. The unbalanced diet was resolved with extra consumption of fruits and dairy products. Conclusions The best meal combination in dine-out menus, even though the proportion and pairing of menus may be unrealistic, is not healthy, and thus one should consume fruits and dairy products to maintain a balanced diet.
The cost of a sewerage system is mainly governed by the size of the sewer pipe, excavation depth and manhole spacing. A linear programming model is developed to minimize the total cost comprising of the pipeline cost,...
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Utilising linear programming techniques in order to estimate the criteria weights based on preferences of decision makers expressed in the form which is used in Simos method usually results in infinite number of optim...
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Utilising linear programming techniques in order to estimate the criteria weights based on preferences of decision makers expressed in the form which is used in Simos method usually results in infinite number of optimal solutions bordered into a n-dimensional hyper-polyhedron. For these cases of low robustness the barycenter is calculated and further used, but cannot always be considered satisfactory as far as the representation of the DM's preferences is concerned. This paper is focused on the presentation of the weights assessment through prioritization method (WAP), constituting a specific integrated implementation of the Robust Simos Method. WAP method on the one hand enriches the preferential information used in a friendly and comprehensive by the DM way while on the other it leads to the estimation of weighting vectors with higher robustness. For the efficient application of the proposed approach, a software module supporting this method was developed and embedded into the RAVI system. The WAP method is presented through an illustration example and the results are discussed in terms of robustness, transparency and comprehensibility.
This paper describes a novel methodology for implementing allpass digital phase compensator (DPC) using the generalized linear-fractional programming (LFP) along with the regularization technique. The allpass DPC desi...
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ISBN:
(数字)9798350381764
ISBN:
(纸本)9798350381771
This paper describes a novel methodology for implementing allpass digital phase compensator (DPC) using the generalized linear-fractional programming (LFP) along with the regularization technique. The allpass DPC design is first stated as a generalized LFP problem, and then it is converted to a regularized minimization problem. This conversion changes the equality constraint in the generalized LFP to an inequality constraint and also adds an extra term to the objective function. The resulting problem reduces to a regularized minimization problem, which can be tackled by using linear programming (LP). That is, the regularized minimization problem reduces to an LP with only inequality design constraints. An allpass DPC example is used to demonstrate that solving the regularized LP yields an optimal solution. The design accuracy and stability issue are also revealed.
We consider the problem of designing output feedback controllers that use measurements from a set of landmarks to navigate through a cell-decomposable environment using duality, Control Lyapunov and Barrier Functions ...
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Facial reduction (FR) is an important tool in linear and semidefinite programming, providing both algorithmic and theoretical insights into these problems. The maximum length of an FR sequence for a convex set is refe...
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