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...ssibilities of extending the method repertoire. An example can be found in Section 6, while in Section 7 we present some test results of GloptLab analyzed by the Test Environment (see Neumaier et al. =-=[24]-=- and Domes et al. [4] for the current version). In the final section we summarize the most important features of GloptLab, give some perspectives and talk about future work. More information is availa...

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...orem of the alternative may serve to define certificates whose presence imply the solvability of one alternative and the unsolvability of the other alternative. Recent advances in global optimization =-=[27, 30]-=- make it possible in many cases to find and verify the global optimality of a solution, or to verify that no feasible point exists. Certificates acquire in this case a special importance, particularly...

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...y, several new methods are developed to solve MINLP problems [18], this includes deterministic algorithms [18], [19] and stochastic ones [20]. The different methods of solving MINLP problems are available through many solvers [21]. The BARON solver [22], which is available through Fig. 2. Centralized implementation of the CORA algorithm. GAMS, is a global deterministic solver which can address nonconvexities in MINLP problems and provide global optima under fairly general assumptions [22]. Since the BARON solver has proven to be the most robust one among the currently available global solvers [23], we use it to solve the radio resource allocation problem of (10). max xnms,bnms N∑ n=1 Sn∑ s=1 ∑ m∈Mns {log(1 + η1xnmsbnms) − η2(1− pnms)xnmsbnms} s.t. ∑ m∈Mns xnmsbnms ≤ Cn, ∀s ∈ Sn, n ∈ N Bminm ≤ N∑ n=1 ∑ s∈Sk xnmsbnms ≤ Bmaxm , ∀m ∈Mk, k ∈ K xnms ∈ {0, 1}, ∀m ∈M1k, k ∈ K N∑ n=1 ∑ s∈Sk xnms = 1, ∀m ∈M1k, k ∈ K xnms = 1, ∀m ∈M2k, k ∈ K. (10) A centralized implementation of the radio resource allocation problem (CORA algorithm) based on the formulation of (10) is illustrated in Figure 2. In this implementation, each MT reports to all BSs/APs available at its location its service type, servic...

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...is the limited amount of supported solvers, restricted to black box optimization. Our approach to developing the Test Environment is inspired by the experience made during the comparisons reported in =-=[19]-=-, in which the Coconut Environment benchmark [22] is run on several di erent solvers. The goal is to create an easy-to-use library and solver management tool, with an intuitive GUI, and an easy, multi...

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... all solutions have been found, and part of the difficulty has been in validation of feasible points. For a more systematic test, we used those problems from the “Tiny 1” Neumaier–Shcherbina test set =-=[7]-=- for which we both had correct Fortran 90 input files 9 and such that we had already implemented rigorous linear relaxations in GlobSol for the standard functions that occurred. For testing Algorithm ...

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...tant current applications of interval analysis include but are not restricted to the following areas (only sample references are given): • global optimization (used in lots of different applications) =-=[31, 40]-=-, • solving equations with multiple solutions (e.g., in chemical engineering [9], computational geometry [7, 35], robotics [24]), • quantified constraint satisfaction [49] (e.g, finding safe work spac...