Class Of Linear Programming Problems Research Articles

An efficient implementable inexact entropic proximal point algorithm for a class of linear programming problems

We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography, and economics. To solve these generally large-scale LP problems efficiently, we design an implementable inexact entropic proximal point algorithm (iEPPA) combined with an easy-to-implement dual block coordinate descent method as a subsolver. Unlike existing entropy-type proximal point algorithms, our iEPPA employs a more practically checkable stopping condition for solving the associated subproblems while achieving provable convergence. Moreover, when solving the capacity constrained multi-marginal optimal transport (CMOT) problem (a special case of our LP problem), our iEPPA is able to bypass the underlying numerical instability issues that often appear in the popular entropic regularization approach, since our algorithm does not require the proximal parameter to be very small in order to obtain an accurate approximate solution. Numerous numerical experiments show that our iEPPA is efficient and robust for solving some large-scale CMOT problems on synthetic data. The preliminary experiments on the discrete tomography problem also highlight the potential modeling capability of our model.

Inference for Large‐Scale Linear Systems With Known Coefficients

This paper considers the problem of testing whether there exists a non‐negative solution to a possibly under‐determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of settings, including random coefficient, treatment effect, and discrete choice models, as well as a class of linear programming problems. As a first contribution, we obtain a novel geometric characterization of the null hypothesis in terms of identified parameters satisfying an infinite set of inequality restrictions. Using this characterization, we devise a test that requires solving only linear programs for its implementation, and thus remains computationally feasible in the high‐dimensional applications that motivate our analysis. The asymptotic size of the proposed test is shown to equal at most the nominal level uniformly over a large class of distributions that permits the number of linear equations to grow with the sample size.

ПРОБЛЕМЫ РАЗВИТИЯ ИНФРАСТРУКТУРЫ ГОРОДСКИХ АГЛОМЕРАЦИЙ

The economic and functional connectivity of the territorial entities included in urban agglomerations creates opportunities for cooperation in the joint implementation of investment projects and targeted programs aimed at the development of infrastructure. It is obvious that the development of infrastructure projects and targeted programs at the preparatory stage involves the formation of a portfolio of facilities services for each territorial entity, taking into account the level of provision of other entities within the boundaries of the urban agglomeration and the volume of own funds and external investments, which include: subsidies allocated from the Federal Fund for Regional Development to the least well-off subjects; investments from budgetary or extra-budgetary funds of higher levels of government; In order to co-finance expenditures in solving issues of local importance, public-private partnerships can also be created and horizontal subsidies provided by one territorial entity to another territorial entity of the same level. In a formalized form, the model of the process of forming a portfolio of service facilities of territorial entities included in the urban agglomeration can be described as follows. It is required to draw up a plan for the commissioning of service facilities that would satisfy the restrictions on investments of two types (own and external) and provide the maximum total effect of the entire system of service objects being created. The mathematical model presented in the article belongs to the class of linear programming problems with Boolean variables and can be solved by an approximate method involving the use of the primitive decomposition method, which significantly reduces the complexity of the solution.

Solution of Large-Scale Linear Programming Problem by Using Computer Technique

Linear programming (LP) is an important part of applied mathematics. This method has found its applications to important areas of product mix, blending, and diet problems. Steel, chemical, food processing industries and Oil refineries industry are also using LP with considerable success. But in practical LP can be very large. In this paper, our intent is to formulate an LP model of some large-scale real-life-oriented problems and to apply computer techniques for solving these problems. Starting with the graphical procedure which provides an ample amount of understanding into some fundamental concepts, the simple procedure of solving LP problems is developed. Finally, a special class of LP problem, namely Transportation is taken up and solved. We also solved the simplex system by using FORTRAN programming.

FUZZY LINEAR PROGRAMMING PROBLEM AND APPLYING NEURAL NETWORKS TO ITS SOLUTION

In present paper consider one economical problem- optimal planning of manufacture. In space of pair of fuzzy numbers this problem formulated as linear programming problem. Applying the certain techniques this problem reduced to classical linear programming problem. Obtained problem solved applying neural networks.

Оптимизация при ограничении числа проектных переменных

A new approach to the formulation and solution of optimization problems of linear and nonlinear type is stated in this article. The problem statement under consideration differs from the classical linear programming problem of the optimal distribution of limited resources between given processes by the need to choose a limited number of processes from a certain finite set and allocate resources over these processes. The goal is to obtain the optimal value of the objective function in relation to other options for choosing the number of processes from the same set and the distribution of resources between them. The objective function can be either linear or non-linear. A nonlinear function must have certain properties for the correct operation of the proposed algorithm for finding the optimal solution. The described method is based on the development of Bellman's ideas of dynamic programming. The proofs of the optimality of the obtained solutions are provided. The article gives an estimate of the computational complexity of the algorithm and a comparison with classical methods for solving the problems under consideration. The types of applied problems solved using the proposed method are characterized. Computer implementations of the described algorithm can be used in automated decision support systems.

Inference for Large-Scale Linear Systems with Known Coefficients

This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of settings, including random coefficient, treatment effect, and discrete choice models, as well as a class of linear programming problems. As a first contribution, we obtain a novel geometric characterization of the null hypothesis in terms of identified parameters satisfying an infinite set of inequality restrictions. Using this characterization, we devise a test that requires solving only linear programs for its implementation, and thus remains computationally feasible in the high-dimensional applications that motivate our analysis. The asymptotic size of the proposed test is shown to equal at most the nominal level uniformly over a large class of distributions that permits the number of linear equations to grow with the sample size.

A Distributed Method for Linear Programming Problems With Box Constraints and Time-Varying Inequalities

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.

Solving linear optimization over arithmetic constraint formula

Since Balas extended the classical linear programming problem to the disjunctive programming (DP) problem where the constraints are combinations of both logic AND and OR, many researchers explored this optimization problem under various theoretical or application scenarios such as generalized disjunctive programming (GDP), optimization modulo theories (OMT), robot path planning, real-time systems, etc. However, the possibility of combining these differently-described but form-equivalent problems into a single expression remains overlooked. The contribution of this paper is two folded. First, we convert the linear DP/GDP model, linear-arithmetic OMT problem and related application problems into an equivalent form, referred to as the linear optimization over arithmetic constraint formula (LOACF). Second, a tree-search-based algorithm named RS-LPT is proposed to solve LOACF. RS-LPT exploits the techniques of interval analysis and nonparametric estimation for reducing the search tree and lowering the number of visited nodes. Also, RS-LPT alleviates bad construction of search tree by backtracking and pruning dynamically. We evaluate RS-LPT against two most common DP/GDP methods, three state-of-the-art OMT solvers and the disjunctive transformation based method on optimization benchmarks with different types and scales. Our results favor RS-LPT as compared to existing competing methods, especially for large scale cases.

Production control system specified quality sausage products

The problem of management of production target in technological system of production of sausages of the set quality is considered in article. Decomposition of technological system is considered. Functions of management are allocated: formation of an optimum compounding of forcemeat, expert analysis of a compounding, laboratory analysis of a compounding and its statement. Information technology of interaction of these functions is offered. The mathematical problem definition of finding of an optimum compounding meat product with use of possible substitutes of ingredients is presented. This mathematical problem is a classical linear programming problem whose solution has the standard program. Since the manufacture of the finished product are various nonlinear effects are taken into account at the present time it is practically impossible, the methodology provided in this operation "Expert analysis of the formulation" and "Laboratory analysis of the finished product." An example of calculating the optimum alternative base recipe "Sausages “Viennese with cheese”" TS 9213-010-40155161-2002. For an alternative formulation demands were made at a cost of meat, the ingredient composition, as well as the final product organoleptic and physic-chemical indicators should comply with regulatory requirements "Sausages “Viennese with cheese”" TS 9213-010-40155161-2002. Indicator acid activity (pH) calculated stuffing formulation should be in the range 6.0-6.3. As a partial replacement for the main raw material have been proposed acceptable substitutes. It was necessary to calculate on the basis of the formulation "Sausages “Viennese with cheese”" TS 9213-010-40155161-2002 optimal price and quality alternative formulation. As a result of depreciation of the value of alternative stuffing recipe was 14,5 % when all of the restrictions on the consumer properties. The proposed information technology implemented in the software package "MultiMeat Expert" and a decision support system for the technology of meat processing enterprise.

Data envelopment analysis and its related linear programming models

We provide a unifying framework synthesizing the dual spaces of production and value used in DEA efficiency measurement with some well-known linear programming (LP) problems. Specifically, we make use of the technology matrix to map intensity variables into input–output space, and the adjoint transformation of the technology matrix to map input–output prices into prices of intensity variables. We show how the diet problem, a classical LP problem, is related to DEA and also use the adjoint matrix to demonstrate a procedure for pricing efficient decision-making units. We further illustrate the relationship between benefit-of-the-doubt aggregation and the diet problem.

Application of linear programming with I-fuzzy sets to matrix games with I-fuzzy goals

In this paper we study a class of linear programming problems having fuzzy goals/constraints that can be described by (Atanassov's) I-fuzzy sets. Duality theory is developed for this class of problems in the I-fuzzy sense which is subsequently applied to define a new solution concept for two persons zero-sum matrix games with I-fuzzy goals.

A Fuzzy LP Approach to Option Portfolio

Abstract: Owing to the fluctuation of financial market from time to time,the volatility and stock price may occur imprecisely in the real world. Therefore, it is natural to consider the fuzzy volatility and fuzzy stock price in the financial market. Under these assumptions,the theoretical price deduced by Black–Scholes formula are will turn into the fuzzy numbers, and the derivatives, called the Greek parameters delta, gamma, of the BS model are also fuzzy numbers. An option portfolio considering these fuzzy numbers will be more accord with actual situations. In this paper, we propose a fuzzy programming model of option portfolio based a ranking criterion of fuzzy numbers, which the fuzzy option portfolio model is converted into a classical linear programming problem. Finally, a numerical example is given to illustrate the validity of the method. Key words: Ranking Criterion; Option portfolio; Fuzzy Linear Programming; Delta-Gamma Neutral

Some Duality Results on Linear Programming Problems with Symmetric Fuzzy Numbers

Recently, linear programming problems with symmetric fuzzy numbers (LPSFN) have considered by some authors and have proposed a new method for solving these problems without converting to the classical linear programming problem, where the cost coefficients are symmetric fuzzy numbers (see in [4]). Here we extend their results and first prove the optimality theorem and then define the dual problem of LPSFN problem. Furthermore, we give some duality results as a natural extensions of duality results for linear programming problems with crisp data.

Optimal decisions in farming management based on methods of operations research - linear multi-criteria multiobject programming.

Linear programming, as a part of applied mathematics, more definitely – the branch of Operations Research, is seen as a solving method of problems linked to optimization. Each economical problem having as a purpose its optimization, especially concerning the distribution of resources, has in wiew the obtaining of an optimal value of a goal, for example a maximum of the profit, or a minimum of the costs. Each economical problem depends of a lot factors submitted to some restrictions (constraints). The goal is dependent of these factors, reason for which the goal is found in a mathematical dependence (function) of these factors, named decisional factors. One has in wiew the optimization of an economic goal represented by a mathematical function of more variables. The optimization function represents a goal from the practice of a large variety of areas:technical, pedagogical, medical, agricultural, personnel organization, etc. The discussed function may be called “purpose function”, or “goal (objective) function”, or “efficiency function”. We prefer the name of “objective function”. If the dependence of the function of the decisional factors is a mathematical linear one (used in the areas mentioned above), then the problem is a linear progamming one. See also the synonymous: objective object. A linear programming problem can be: a “classical linear programming problem”, a “multi-criteria multiobject problem”, or a “transport problem”. In the paper is presented only the “multi-criteria multiobject problem”. Is presented the mathematical pattern, the coresponding terminology and also some practical issued solved on the computer in the summaries submitted to the work. Supplementary, we have to mentioned that the author is the holder of the implementations on computer of the pattern mentioned above, in both known programming environment Fortran 77, C++ and desk computer one. See [8] and [9] from bibliography. See also [1], [2], [5] and [6].

Optimization of the structure of production systems

It is shown that optimal solutions for a class of linear programming problems with partially integer variables (the PILP problems) can be constructed at the first stage of the Danzig-Wolfe decomposition [1]. Using this result allows one to simplify sufficiently the structure of production systems independently of the dimension of an initial problem.

Rounding of convex sets and efficient gradient methods for linear programming problems

In this paper, we propose new efficient gradient schemes for two non-trivial classes of linear programming problems. These schemes are designed to compute approximate solutions with relative accuracy δ. We prove that the upper complexity bound for both schemes is O((√(n ln m)/δ)ln n) iterations of a gradient-type method, where n and m (n<m) are the sizes of the corresponding linear programming problems. The proposed schemes are based on preliminary computation of an ellipsoidal rounding for some polytopes in R n . In both cases, this computation can be performed very efficiently, in O(n 2 m ln m) operations at most.

Quadratic approximation of penalty functions for solving large-scale linear programs

Using the least squares, modified Lagrangian function, and some other methods as examples, the capabilities of the new optimization technique based on the quadratic approximation of penalty functions that has been recently proposed by O. Mangasarian for a special class of linear programming problems are demonstrated. The application of this technique makes it possible to use unified matrix operations and standard linear algebra packages (including parallel ones) for solving large-scale problems with sparse strongly structured constraint matrices. With this technique, the computational schemes of some well-known algorithms can take an unexpected form.

Fuzzy stochastic linear programming: Survey and future research directions

In many real-life problems one has to base decision on information which is both fuzzily imprecise and probabilistically uncertain. Although consistency indexes providing a union nexus between possibilistic and probabilistic representation of uncertainty exist, there are no reliable transformations between them. This calls for new paradigms for incorporating the two kinds of uncertainty into mathematical models. Fuzzy stochastic linear programming is an attempt to fulfill this need. It deals with modelling and problem solving issues related to situations where randomness and fuzziness co-occur in a linear programming framework. In this paper we provide a survey of the essential elements, methods and algorithms for this class of linear programming problems along with promising research directions. Being a survey, the paper includes many references to both give due credit to results in the field and to help readers obtain more detailed information on issues of interest.

A linear programming procedure based on de la Vallée Poussin's minimax estimation procedure

It is shown that de la Vallée Poussin's 1911 procedure for the solution of linear minimax estimation problems can be adjusted to solve a class of linear programming problems. A general procedure of this type should have been accessible in the 1910s, but the historical record shows that no such procedure was developed before the work of Kantorovich, Koopmans, and Dantzig in the 1940s.