- Bulletin of the Iranian Mathematical Society
... where nj − 1 < βj ≤ nj . By substituting Eqs. (4.8)-(4.10) in Eq. (1.1), we obtain a system of algebraic equations, which can be solved to find unknown function. Implementation of this approach is given in the next section via numerical experiments. 5. Applications and results In this section we ill ...
... where nj − 1 < βj ≤ nj . By substituting Eqs. (4.8)-(4.10) in Eq. (1.1), we obtain a system of algebraic equations, which can be solved to find unknown function. Implementation of this approach is given in the next section via numerical experiments. 5. Applications and results In this section we ill ...
MAT-52506 Inverse Problems
... We look for a reconstruction procedure R : Rk → Rn that would satisfy R(m) ≈ x, the approximation being better when the size ε of the noise is small. The connection between R and Hadamard’s notions is as follows: m is the input and R(m) is the output. Now (1.1) means that the function R should be ...
... We look for a reconstruction procedure R : Rk → Rn that would satisfy R(m) ≈ x, the approximation being better when the size ε of the noise is small. The connection between R and Hadamard’s notions is as follows: m is the input and R(m) is the output. Now (1.1) means that the function R should be ...
price-based market clearing under marginal pricing: a
... Thus, after some algebra, problem (21)-(28) is recast as a mixed-integer linear programming problem suitable for commercially available branch-and-cut software. 4 APPLICATION To illustrate the above bilevel programming framework, we now consider an instance of price-based market clearing, namely the ...
... Thus, after some algebra, problem (21)-(28) is recast as a mixed-integer linear programming problem suitable for commercially available branch-and-cut software. 4 APPLICATION To illustrate the above bilevel programming framework, we now consider an instance of price-based market clearing, namely the ...
![[SE4] Integral simplex using decomposition for the set partitioning](http://s1.studyres.com/store/data/019693331_1-53981937bc1c58ca78e99eb6a82baf81-300x300.png)
[SE4] Integral simplex using decomposition for the set partitioning
... proved the existence of such a sequence with nonincreasing costs, but degeneracy makes it difficult to find the terms of the sequence. This paper uses ideas from the improved primal simplex to deal efficiently with degeneracy and find subsequent terms in the sequence. When there is no entering varia ...
... proved the existence of such a sequence with nonincreasing costs, but degeneracy makes it difficult to find the terms of the sequence. This paper uses ideas from the improved primal simplex to deal efficiently with degeneracy and find subsequent terms in the sequence. When there is no entering varia ...
Binary Integer Programming in associative data models
... Given an objective function F defined on a set Ω with range Φ, an element in Ω corresponding to such a solution can be denoted argopt. Then we arrive at the following definition: Definition 1.1. An optimization problem is to find e x such that: e x = argopt x∈Ω ...
... Given an objective function F defined on a set Ω with range Φ, an element in Ω corresponding to such a solution can be denoted argopt. Then we arrive at the following definition: Definition 1.1. An optimization problem is to find e x such that: e x = argopt x∈Ω ...
A New Discontinuous Petrov-Galerkin Method with Optimal Test
... The Discontinuous Petrov-Galerkin method introduced by Demkowicz and Gopalakrishnan in [13, 14, 15] (DPG), falls under the DG category, but avoids the restrictions and stabilizing parameters of the previous methods. Inherent in the DPG is not only the flexibility of DG, but a stronger proven stabili ...
... The Discontinuous Petrov-Galerkin method introduced by Demkowicz and Gopalakrishnan in [13, 14, 15] (DPG), falls under the DG category, but avoids the restrictions and stabilizing parameters of the previous methods. Inherent in the DPG is not only the flexibility of DG, but a stronger proven stabili ...
Design of an efficient algorithm for fuel-optimal look-ahead
... For mixed-integer nonlinear optimization, a complex combinatorial problem typically arises with the open-loop approaches due to the integer variables (Floudas, 1995). For DP, however, the computational complexity is linear in the horizon length which is beneficial for this application since a rather ...
... For mixed-integer nonlinear optimization, a complex combinatorial problem typically arises with the open-loop approaches due to the integer variables (Floudas, 1995). For DP, however, the computational complexity is linear in the horizon length which is beneficial for this application since a rather ...
Multiple-criteria decision analysis
Multiple-criteria decision-making or multiple-criteria decision analysis (MCDA) is a sub-discipline of operations research that explicitly considers multiple criteria in decision-making environments. Whether in our daily lives or in professional settings, there are typically multiple conflicting criteria that need to be evaluated in making decisions. Cost or price is usually one of the main criteria. Some measure of quality is typically another criterion that is in conflict with the cost. In purchasing a car, cost, comfort, safety, and fuel economy may be some of the main criteria we consider. It is unusual that the cheapest car is the most comfortable and the safest one. In portfolio management, we are interested in getting high returns but at the same time reducing our risks. Again, the stocks that have the potential of bringing high returns typically also carry high risks of losing money. In a service industry, customer satisfaction and the cost of providing service are two conflicting criteria that would be useful to consider.In our daily lives, we usually weigh multiple criteria implicitly and we may be comfortable with the consequences of such decisions that are made based on only intuition. On the other hand, when stakes are high, it is important to properly structure the problem and explicitly evaluate multiple criteria. In making the decision of whether to build a nuclear power plant or not, and where to build it, there are not only very complex issues involving multiple criteria, but there are also multiple parties who are deeply affected from the consequences.Structuring complex problems well and considering multiple criteria explicitly leads to more informed and better decisions. There have been important advances in this field since the start of the modern multiple-criteria decision-making discipline in the early 1960s. A variety of approaches and methods, many implemented by specialized decision-making software, have been developed for their application in an array of disciplines, ranging from politics and business to the environment and energy.