An Eulerian-Lagrangian method for optimization problems governed
... If = R2 , then (1.1b) is supplemented by appropriate boundary conditions. In recent years, there has been tremendous progress in both analytical and numerical studies of problems of type (1.1a), (1.1b), see, e.g., [1–3,8–10,13,18,19,21– 24,28,40,44,45]. Its solution relies on the property of the ...
... If = R2 , then (1.1b) is supplemented by appropriate boundary conditions. In recent years, there has been tremendous progress in both analytical and numerical studies of problems of type (1.1a), (1.1b), see, e.g., [1–3,8–10,13,18,19,21– 24,28,40,44,45]. Its solution relies on the property of the ...
Multiuser MISO Beamforming for Simultaneous
... and show that under the condition of independently distributed user channels, the SDRs are tight for the formulated non-convex QCQPs. It is revealed that for the case of Type I ID receivers, no dedicated energy beam is used to achieve the optimal solution, while for the case of Type II ID receivers, ...
... and show that under the condition of independently distributed user channels, the SDRs are tight for the formulated non-convex QCQPs. It is revealed that for the case of Type I ID receivers, no dedicated energy beam is used to achieve the optimal solution, while for the case of Type II ID receivers, ...
Document
... The penalty incurred by additional space in a gap decrease as the gap gets longer. Example: the logarithmic gap penalty g(q) = a log q + b ...
... The penalty incurred by additional space in a gap decrease as the gap gets longer. Example: the logarithmic gap penalty g(q) = a log q + b ...
The theory of optimal stopping
... sample as well as for ultimately taking an incorrect decision. The desire is to taka as few samples as possible while choosing between H0 and H1 witl1 the best confidence possible. The search is essentially for a time, t, which teL1s us when to stop sampl.ing and a decision rule, 6, which ·then tell ...
... sample as well as for ultimately taking an incorrect decision. The desire is to taka as few samples as possible while choosing between H0 and H1 witl1 the best confidence possible. The search is essentially for a time, t, which teL1s us when to stop sampl.ing and a decision rule, 6, which ·then tell ...
2.1 Pairwise Alignment
... Proof: [3] (chapter 12) For any xed position k 0 in T , there is an alignment of S and T consisting of an alignment of S1 : : :S 2 and T1 : : : Tk0 followed by a disjoint alignment of S 2 +1 : : :Sn and Tk0 +1 : : : Tm. By de nition of V and V r , the best alignment of the rst type has value V ( n ...
... Proof: [3] (chapter 12) For any xed position k 0 in T , there is an alignment of S and T consisting of an alignment of S1 : : :S 2 and T1 : : : Tk0 followed by a disjoint alignment of S 2 +1 : : :Sn and Tk0 +1 : : : Tm. By de nition of V and V r , the best alignment of the rst type has value V ( n ...
Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other. A computational problem is understood to be a task that is in principle amenable to being solved by a computer, which is equivalent to stating that the problem may be solved by mechanical application of mathematical steps, such as an algorithm.A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying the amount of resources needed to solve them, such as time and storage. Other complexity measures are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of computational complexity theory is to determine the practical limits on what computers can and cannot do.Closely related fields in theoretical computer science are analysis of algorithms and computability theory. A key distinction between analysis of algorithms and computational complexity theory is that the former is devoted to analyzing the amount of resources needed by a particular algorithm to solve a problem, whereas the latter asks a more general question about all possible algorithms that could be used to solve the same problem. More precisely, it tries to classify problems that can or cannot be solved with appropriately restricted resources. In turn, imposing restrictions on the available resources is what distinguishes computational complexity from computability theory: the latter theory asks what kind of problems can, in principle, be solved algorithmically.