This paper presents a study done to find an interior point in the feasible region of linear programming problems is an aspect that should be solved in the initial stage of the implementation of the interior point algo...
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This paper presents a study done to find an interior point in the feasible region of linear programming problems is an aspect that should be solved in the initial stage of the implementation of the interior point algorithms used to optimize them. Consequently, it is proposed a methodology that starts with a formulation that does not require adding surplus or slack variables. It only includes an additional variable to generate a polyhedron in a new expanded space and with simple projections finds an interior point in the same polyhedron. It is demonstrated that the optimal solution of the extended linear programming problem allows obtaining a feasible point of the original problem or concluding that it has no feasible solutions.
We consider the problem of tracking a target whose dynamics is modeled by a continuous Ito semi-martingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asy...
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We consider the problem of tracking a target whose dynamics is modeled by a continuous Ito semi-martingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asymptotic lower bounds for this problem, depending on the cost structure. These lower bounds can be related to the time-average control of Brownian motion, which is characterized as a deterministic linear programming problem. A comprehensive list of examples with explicit expressions for the lower bounds is provided.
A decision-support tool (ORES) in the form of a linear program is developed to determine the optimal investment and operating decisions for residential energy systems. It shows how energy conversion units such as a co...
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A decision-support tool (ORES) in the form of a linear program is developed to determine the optimal investment and operating decisions for residential energy systems. It shows how energy conversion units such as a cogeneration fuel cell, a heat pump, a boiler, photovoltaic panels and solar thermal collectors can be combined with energy storage devices, consisting of a battery and a hot water tank, to drive down total yearly energy costs and CO2 emissions while meeting space heat, hot water and electricity needs. Under the assumption of perfect demand and production forecasts and depending on how the dwelling is allowed to exchange electricity with the grid, cost reductions between 5 and 60% are possible, whereas emissions can be cut by 45-90% with respect to a base case. Stochastic programming is used effectively to reduce the sensitivity to uncertainty in weather parameters. The resulting cost increase is limited to 1.2%. Decision rules are implemented to account for unforeseen variations in electric load. If it is assumed that peak loads can occur at any instant of the optimization horizon, energy costs rise by 9%, which in off-grid scenarios, are driven by the installation of an about 50% bigger battery system. (C) 2016 Elsevier Ltd. All rights reserved.
Recently, Wang et al. [IEEE INFOCOM 2011, 820-828], and Nie et al. [IEEE AINA 2014, 591-596] have proposed two schemes for secure outsourcing of linear programming (LP). They did not consider the standard form: minimi...
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Recently, Wang et al. [IEEE INFOCOM 2011, 820-828], and Nie et al. [IEEE AINA 2014, 591-596] have proposed two schemes for secure outsourcing of linear programming (LP). They did not consider the standard form: minimize cTx, subject to Ax = b, x ≥ 0. Instead, they studied a peculiar form: minimize cTx, subject to Ax = b, Bx ≥ 0, where B is a non-singular matrix. In this note, we stress that the proposed peculiar form is unsolvable and meaningless. The two schemes have confused the functional inequality constraints Bx ≥ 0 with the nonnegativity constraints x ≥ 0 in the linear programming model. But the condition x ≥ 0 is indispensable to LP. Thus, both two schemes failed.
We describe an iterative refinement procedure for computing extended-precision or exact solutions to linear programming (LP) problems. Arbitrarily precise solutions can be computed by solving a sequence of closely rel...
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We describe an iterative refinement procedure for computing extended-precision or exact solutions to linear programming (LP) problems. Arbitrarily precise solutions can be computed by solving a sequence of closely related LPs with limited-precision arithmetic. The LPs solved share the same constraint matrix as the original problem instance and are transformed only by modification of the objective function, right-hand side, and variable bounds. Exact computation is used to compute and store the exact representation of the transformed problems, and numeric computation is used for solving LPs. At all steps of the algorithm the LP bases encountered in the transformed problems correspond directly to LP bases in the original problem description. We show that this algorithm is effective in practice for computing extended-precision solutions and that it leads to direct improvement of the best known methods for solving LPs exactly over the rational numbers. Our implementation is publically available as an extension of the academic LP solver SOPLEX.
Bilevel linear optimization problems are the linear optimization problems with two sequential decision steps of the leader and the follower. In this paper, we focus on the ambiguity of coefficients of the follower in ...
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Bilevel linear optimization problems are the linear optimization problems with two sequential decision steps of the leader and the follower. In this paper, we focus on the ambiguity of coefficients of the follower in his objective function that hinder the leader from exactly calculating the rational response of the follower. Under the assumption that the follower's possible range of the ambiguous coefficient vector is known as a certain convex polytope, the leader can deduce the possible set of rational responses of the follower. The leader further assumes that the follower's response is the worst-case scenario to his objective function, and then makes a decision according to the maximin criteria. We thus formulate the bilevel linear optimization problem with ambiguous objective function of the follower as a special kind of three-level programming problem. In our formulation, we show that the optimal solution locates on the extreme point and propose a solution method based on the enumeration of possible rational responses of the follower. A numerical example is used to illustrate our proposed computational method.
This paper presents a new idea to solve fractional differential equations and fractional optimal control problems. The fractional derivative is defined in the Grunwald-Letnikov sense. The method is based on the linear...
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This paper presents a new idea to solve fractional differential equations and fractional optimal control problems. The fractional derivative is defined in the Grunwald-Letnikov sense. The method is based on the linear programming problem. In this paper, by using first the concept of fractional derivatives, we will suggest a method where an equation with a fractional derivative is changed to a linear programming problem, and by solving it the fractional derivative will be obtained. Actually this suggested method is based on the minimization of total error. Some numerical examples are provided to confirm the accuracy of the proposed method.
This paper introduces the concept of critical objective size associated with a linear program in order to provide operative point-based formulas (only involving the nominal data, and not data in a neighborhood) for co...
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This paper introduces the concept of critical objective size associated with a linear program in order to provide operative point-based formulas (only involving the nominal data, and not data in a neighborhood) for computing or estimating the calmness modulus of the optimal set (argmin) mapping under uniqueness of nominal optimal solution and perturbations of all coefficients. Our starting point is an upper bound on this modulus given in Canovas et al. (2015). In this paper we prove that this upper bound is attained if and only if the norm of the objective function coefficient vector is less than or equal to the critical objective size. This concept also allows us to obtain operative lower bounds on the calmness modulus. We analyze in detail an illustrative example in order to explore some strategies that can improve the referred upper and lower bounds.
Considering the ever changing market conditions, it is essential to design responsive and flexible manufacturing systems. This study addresses the multi-period Dynamic Cellular Manufacturing System (DCMS) design probl...
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Considering the ever changing market conditions, it is essential to design responsive and flexible manufacturing systems. This study addresses the multi-period Dynamic Cellular Manufacturing System (DCMS) design problem and introduces a new mathematical model. The objective function of the mathematical model considers inter-cell and intra-cell material handling, machine purchasing, layout reconfiguration, variable and constant machine costs. Machine duplication, machine capacities, operation sequences, alternative processing routes of the products, varying demands of products and lot splitting are among the most important issues addressed by the mathematical model. It makes decisions on many system related issues, including cell formation, inter- and intra-cell layout, product routing and product flow between machines. Due to the complexity of the problem, we suggest two heuristic solution approaches that combine Simulated Annealing (SA) with linear programming and Genetic Algorithm (GA) with linear programming. The developed approaches were tested using a data set from the literature. In addition, randomly generated test problems were also used to investigate the performance of the hybrid heuristic approaches. A problem specific lower bound mathematical model was also proposed to observe the solution quality of the developed approaches. The suggested approaches outperformed the previous study in terms of both computational time and the solution quality by reducing the overall system cost. (C) 2015 Elsevier Ltd. All rights reserved.
This paper proposes a linear programming (LP) approach for stabilization of positive Markovian jump systems (PMJSs) with input saturation. First of all, we derive the sufficient conditions for stabilization of PMJSs w...
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ISBN:
(纸本)9784907764579
This paper proposes a linear programming (LP) approach for stabilization of positive Markovian jump systems (PMJSs) with input saturation. First of all, we derive the sufficient conditions for stabilization of PMJSs with input saturation based on the linear co-positive Lyapunov function. However, since the decision variables in the obtained conditions are mutually coupled, the conditions are not linear. Therefore, to obtain the condition that can be solved by the LP, we propose the methods to properly choose the decision variables. Furthermore, we give a process to acquire the largest domain of attraction. Finally, we suggest two numerical examples to illustrate the validity of the proposed methods.
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