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Statistical Analysis and Computer Simulation
Published in Goff Hill, The Cable and Telecommunications Professionals' Reference, 2012
Fraidoon Mazda, David K. Hunter
It is important to verify that a simulation program is producing reliable results. However, it is never possible to be absolutely certain that it is correct. It is merely possible to establish a greater or lesser degree of confidence in the simulator. One way of doing so is to check as many of the programmer's unconscious assumptions as possible by placing assertions in the code. For example, check that a packet must be present in the server before service can begin, and that queue lengths must not be negative. Assertions can be checked at run time during program development, then switched off (if necessary) for efficiency during program execution. Alternatively, analytical checks can be made by running the simulator under restricted or boundary conditions on a problem that can be solved analytically. It is also possible to run the simulator on a problem for which simulation results from another simulator already exist. In either case, the simulator results (from several runs) can be compared with the known results using the appropriate statistical tests.
Space applications of system of systems
Published in Mo Jamshidi, Systems of Systems Engineering, 2017
Dale S. Caffall, James Bret Michael
We propose the use of assertions in the development of formal specifications. Assertions can help system engineers find defects in specifications and designs earlier than they would otherwise find errors and greatly reduce the incidence of mistakes in interpreting and implementing correct requirements and designs. Additionally, the development and verification of formal specifications can support the development of error-handling specifications to appropriately manage runtime errors and logic breaks.
Formal Methods
Published in Phillip A. Laplante, Requirements Engineering for Software and Systems, 2017
To deal with this situation, we need to define assertions. An assertion is some relation that is true at that instant in the execution of the program. An assertion preceding a statement in a program is called a precondition of the statement. An assertion following a statement is called a postcondition. Certain programming languages, such as Eiffel and Java, incorporate run-time assertion checking. Assertions are also used for testing fault tolerance (through fault-injection).
Simplified versions of the conditional gradient method
Published in Optimization, 2018
It was observed in Section 2 that the usual CGM attains the convergence rate under the additional assumptions that the function f is convex and its gradient is Lipschitz continuous (see Proposition 2.5 and formula 8). This means that the total number of iterations that is necessary for attaining some prescribed accuracy for the gap value is estimated as follows: We can try to obtain a similar estimate for CGMI with the proper specialization. In fact, if the gradient of the function f is Lipschitz continuous on D with some constant L>0, we can take the well-known property of such functions see [3, Chapter III, Lemma 1.2]. Then, at Step 2 we have if . Note that at stage p, hence the right value in the above inequality is positive, besides, . If we simply take with and then as desired, cf. (15). This means that we can drop the line-search procedure in Step 2. We call this modification CGMIL. Obviously, the assertions of Proposition 4.2 and Theorem 4.3 remain true for this version.
Error bounds revisited
Published in Optimization, 2022
Nguyen Duy Cuong, Alexander Y. Kruger
The assertions in the next proposition are extracted from [9, Proposition 4.5 & Theorem 4.7] and their proofs. The set of active indices at is defined by The problem satisfies the Slater condition if there exists an such that for all .
Finite dimensional approximations for a class of infinite dimensional time optimal control problems
Published in International Journal of Control, 2019
Marius Tucsnak, Julie Valein, Chi-Ting Wu
We recall that z, solution of system (1.1)–(1.2), satisfies (1.3) and zh, solution of (1.5)–(1.6), satisfies (1.9). It is clear that By using assertions (5) and (7) in Proposition3.2, we have: This ends the proof.