Environmental watering in the Murray-Darling Basin often entails releasing water from upstream storages to achieve a downstream high flow target. This is to induce strategic inundation of riparian wetlands for improve...
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The paper is devoted to the construction of an algorithm for solving an optimization logistic problem with a quadratic objective function. This problem is a quadratic programming problem with constraints such as equal...
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The paper is devoted to the construction of an algorithm for solving an optimization logistic problem with a quadratic objective function. This problem is a quadratic programming problem with constraints such as equalities and inequalities. One of the constraints contains a parameter. The solution of the problem needs to be obtained in general form for any parameter value. In the process of constructing the algorithm, the concept of corner points is introduced. The solution of the problem is reduced to finding a finite set of corner points. All other optimal solutions are represented as linear combinations of two corner points. The constructed algorithm is implemented on a test example.
The energetic crisis jeopardizes the safety of nations and people in multiple ways. In addressing the problem of commodity production out of feedstock imports, an eco-environmentally rational agent aims at minimizing ...
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The energetic crisis jeopardizes the safety of nations and people in multiple ways. In addressing the problem of commodity production out of feedstock imports, an eco-environmentally rational agent aims at minimizing the cost of feedstock imports and their increasingly expensive transportation, but also the water footprint of the feedstock production process and the water scarcity in the exporting countries. This implies the need for more accurate feedstock import strategies, that account for the increased multiplicity of factors at play. This study proves the existence of solutions and quantitatively demonstrates that transportation costs and non-uniform feedstock characteristics inhibit feedstock interchangeability, by solving a novel nonlinear program that accounts for the complexity of the factors at play. Moreover, it is shown that the interplay between water footprint and water scarcity across countries can inhibit or foster feedstock interchangeability. Model validation strategies and a sensitivity analysis complete the study.
New vapor-liquid equilibrium (VLE) data are continuously being measured and new parameter values, e.g., for the nonrandom two-liquid (NRTL) model are estimated and published. The parameter α, the nonrandomness parame...
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Necessary optimality conditions in Lagrangian form and the augmented Lagrangian framework are extended to mixed-integer nonlinear optimization, without any convexity assumptions. Building upon a recently developed not...
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Binaural reproduction for headphone-centric listening has become a focal point in ongoing research, particularly within the realm of advancing technologies such as augmented and virtual reality (AR and VR). The demand...
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The presented paper considers the pricing and lot-sizing decisions for a manufacturer who produces and sells a single product in different selling channels i.e physical stock, website, mobile, etc. The objective is to...
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The presented paper considers the pricing and lot-sizing decisions for a manufacturer who produces and sells a single product in different selling channels i.e physical stock, website, mobile, etc. The objective is to find the production plan and prices of each channel to maximize the total profit defined from difference between the revenues and the productions, holding and setups costs. The consumers' demand in each channel is represented by attraction demand models which include the multinomial logit (MNL), multiplicative competitive interaction (MCI) and linear demand models. The addressed problem is formulated as a non -convex mixed-integer nonlinear program (MINLP). Based on properties of attraction functions, an efficient reformulation which transforms the initial non-convex problem into a convex one is presented. Therefore, an optimization approach based on the outer approximation algorithm is presented to solve the problem. Numerical tests based on large benchmark of real inspired instances show the efficiency of the proposed approach to solve the addressed problem compared to the initial non-convex model.
We investigate a solution of a convex programming problem with a strongly convex objective function based on the dual approach. A dual optimization problem has constraints on the positivity of variables. We study the ...
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We investigate a solution of a convex programming problem with a strongly convex objective function based on the dual approach. A dual optimization problem has constraints on the positivity of variables. We study the methods and properties of transformations of dual variables that enable us to obtain an unconstrained optimization problem. We investigate the previously known method of transforming the components of dual variables in the form of their modulus (modulus method). We show that in the case of using the modulus method, the degree of the degeneracy of the function increases as it approaches the optimal point. Taking into account the ambiguity of the gradient in the boundary regions of the sign change of the new dual function variables and the increase in the degree of the function degeneracy, we need to use relaxation subgradient methods (RSM) that are difficult to implement and that can solve non-smooth non-convex optimization problems with a high degree of elongation of level surfaces. We propose to use the transformation of the components of dual variables in the form of their square (quadratic method). We prove that the transformed dual function has a Lipschitz gradient with a quadratic method of transformation. This enables us to use efficient gradient methods to find the extremum. The above properties are confirmed by a computational experiment. With a quadratic transformation compared to a modulus transformation, it is possible to obtain a solution of the problem by relaxation subgradient methods and smooth function minimization methods (conjugate gradient method and quasi-Newtonian method) with higher accuracy and lower computational costs. The noted transformations of dual variables were used in the program module for calculating the maximum permissible emissions of enterprises (MPE) of the software package for environmental monitoring of atmospheric air (ERA-AIR).
The paper presents three methods for data classification and finding the optimal plan: the study of the quadratic programming problem, the double problem and the Support Vector Machine method. It is known that linear ...
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The paper presents three methods for data classification and finding the optimal plan: the study of the quadratic programming problem, the double problem and the Support Vector Machine method. It is known that linear programming is used to solve resource allocation problems. Also, its purpose is widely used to determine the highest profit or lowest cost, inventory management, the formation of an optimal transportation plan or to determine research, and so on. An important approach to the application of linear programming problems is the use of the duality principle, which is methodologically related to the theory of systems of dependent inequalities. This aspect better explains the concept of duality in linear programming problems with general mathematical rigor.
Genetic algorithms have unique advantages in dealing with optimization problems. In this paper the main focus is on the improvement of a genetic algorithm and its application in nonlinear programming problems. In the ...
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