In the problem formulation, it is evident that both types of constraints are also functioning of x, so it is safe to say that the constraints are only applied to the inputs of an optimization system. The preceding two examples classified optimization problems into two classes: unconstrained and...
A maximization problem in tropical mathematics: A complete solution and application examples. Informatica, 2016, vol. 27, no. 3, pp. 587-606. DOI:10.15388/Informatica.2016.101N. Krivulin, “A constrained tropical optimization problem: Complete solution and application example,” in Tropical and ...
The necessary conditions for optimality are explained and illustrated with examples. All optimum designs must satisfy these conditions. The standard design optimization model introduced in Section 2.11 is restated in Table 4-2. The inequality constraints of Eq. (4.39) will be initially ignored to ...
The main result provides the conditions under which these solutions converge to the minimizer of the limit problem. The generality of the result allows its application to a wide range of problems: elliptic, parabolic, control ones, etc. The examples presented in the paper consider optimal ...
The proposed method relies on a suitable local optimization procedure, yielding an efficient recipe for the realistic and approximate sequential generation of any entangled multiqubit state. We give paradigmatic examples that may be of interest for theoretical and experimental developments. 展开 ...
Prime examples of GNN applications includeclassification of users in social networks [30, 31], theprediction of future interactions in recommender systems[32], and the prediction of certain properties of moleculargraphs [33, 34]. 从本质上讲,GNN 是专门为图结构数据设计的深度神经网络架构,能够学习...
In this section, we give two numerical examples to demonstrate the obtained theoretic results. Example 5.1 This example shows that the primal–dual algorithm with constant step size can produce the accurate estimates for the constrained optimization problem, where gradients of the cost functions are...
We prove that the differential equations locally converge to a constrained\udminimum.\ud\udExamples of applications of the differential method of multipliers include enforcing permutation\udcodewords in the analog decoding problem and enforcing valid tours in the traveling salesman problem. 展开 ...
However, nonconvexity of the nonlinear programs (NLP) involved in the MPC optimization makes the solution problematic. In order to explore properties of MPC-based constrained control schemes, and to point out the potential issues in implementing MPC, challenging benchmark examples are generated and ...
The chapter also discusses three examples of constrained optimization problems in a function space setting—problem concerning evasive tactics, problem in production scheduling, and problem in rocketry. Gateaux differential and gradients in function space are introduced in the chapter to establish a ...