By Richard Kaiser
ISBN-10: 3540629947
ISBN-13: 9783540629948
Dieses Buch verbindet eine systematische Einf?hrung in die Programmiersprache C++ mit der Vorstellung des C++Builders von Borland. Dieses visuelle Entwicklungssystem f?r Windows-Programme ist die Variante C++ von Delphi. Alle Sprachelemente und Konzepte von C++ nach dem C++-Standard werden ausf?hrlich und praxisnah behandelt. Besondere Schwerpunkte sind die Themen objektorientierte Programmierung in Verbindung mit objektorientierter examine und layout, Exception-Handling, Templates und ihre Anwendungen am Beispiel der Klassen und Algorithmen der STL. Das Buch wendet sich sowohl an Anf?nger als auch an erfahrene C++-Programmierer und enth?lt zahlreiche Beispiele und ?bungsaufgaben. Es enth?lt auf der beiliegenden CD eine freie model des C++ developers und L?sungen der ?bungsaufgaben.
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Sample text
It highly depends on properties of the central path of (SP), which is introduced in the next section. 14) that 5(e) = e, where e (as always) denotes the all-one vector of appropriate length (in this case, n). 27) Now we come to a very fundamental notion, both from a theoretical and algorithmic point of view, namely the central path of the LO-problem at hand. 12, find the set of all optimal solutions and the optimal partition. ^^ Exercise 5 Same as in Exercise 4, but now with 11 h \^ 2] ^^ Exercise 6 Same as in Exercise 4, but now with [2 /3>0.
13) with 1^ = 0 and K. > 0. For that purpose we consider another self-dual embedding of (P) and (D), namely (SP) min {q^z : Mz>-q,z>0}. 16) The following theorem shows that we can achieve our goal by solving this problem. 13) has a solution with 1^ = 0 and K. > 0 if and only if the problem (SP) has an optimal solution with n = Zn-i > 0Proof: Since q>0 and z > 0, we have q^z > 0, and hence the optimal value of (SP) is certainly nonnegative. On the other hand, since q > 0 the zero vector {z = 0) is feasible, and yields zero as objective value, which is therefore the optimal value.
Let us call an LO-problem solvable if it has an optimal solution, and unsolvable otherwise. Note that an LO-problem can be unsolvable for two possible reasons: the domain of the problem is empty, or the domain is not empty but the objective function is unbounded on the domain. In the first case the problem is called infeasible and in the second case unbounded. 25 If n ^ N then neither {P) nor {D) has an optimal solution. Proof: Let n G N. 24 we then have vectors x and y such that X > 0, 7/ > 0, Ax>0, A^y < 0, b^y - c^x > 0.
C++ mit dem Borland C++ Builder by Richard Kaiser
by Richard
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