After offering an overview of some of the main themes of Popper’s political thought, the paper argues that his account faces two problems relating to institutions. The first is that while Popper stresses the ‘rational unity of mankind’, and the potential for any of us to furnish criticisms of public policy, it is not clear what institutional means currently exist for this to enable this to take place. Second, Popper has stressed the conjectural character of even our best theories. However, at any point, some theories will have fared better in the face of criticism than others, and they may give us important information about constraints on our actions. At the same time, as ordinary citizens we may not be in a good position to understand the theories in question, let alone appraise the state of the specialised discussion of them. There is, it is suggested, a case for thinking of ways to institutionally entrench such fallible theories, especially in the current setting in which social media play an important role

Application of the network equivalent concept for external system representation for power system transient analysis is well known. However, the challenge to utilize an equivalent network, approximated by a rational function, is to guarantee the passivity of the corresponding model. In this regard, special techniques are required to enforce the passivity of the equivalent model through a post processing approach that minimizes its impact on the original model characteristics. In this paper, the passivity is enforced by expressing the problem in terms of a convex optimization problem that guarantees the global optimal solution. The convex optimization problem is efficiently solved by recently developed numerical interior–point methods. This passivity enforcement is also global which indicates that the passivity enforcement in one region does not lead to passivity violation in other regions.

The aim of this paper is to establish sequential necessary and sufficient approximate optimality conditions for a constrained convex vector mini-mization problem without any constraint qualifications, characterizing the approximate proper and weak efficient solutions. The constraints are de-scribed by mappings taking values in different preorder vector spaces. Our approach is based essentially on the sequential approximate subdifferential calculus rule for the sums of a finite family of cone convex mappings. To illustrate our main result, an application to multiobjective fractional pro-gramming problem is given. Finally, we present an important subclass of such problems showing the applicability of the obtained conditions.

In this paper, we present an improved neural network to solve strictly convex quadratic program-ming(QP) problem. The proposed model includes a set of di erential equations such that their equi-librium points correspond to optimality condition of convex (QP) problem and has a lower structure complexity respect to the other existing neural network model for solving such problems. In theoret-ical aspect, stability and global convergence of the proposed neural network is proved. The validity and transient behavior of the proposed neural network are demonstrated by using four numerical examples.

In this paper the recently developed meta-heuristic optimization method, known as charged system search (CSS), is utilized for optimum nodal ordering to minimize bandwidth and profile of sparse matrices. The CSS is an optimization algorithm, which is based on the governing laws of Coulomb and Gauss from electrostatics and the Newtonian mechanics of motion. The bandwidth and profile of some graph matrices, which are pattern equivalent to structural matrices, are minimized using this approach. This shows the applicability of the meta-heuristic algorithms in bandwidth and profile optimization. Comparison of the results with those of some existing methods, confirms the robustness of the new algorithm.

In the proposed manuscript, the solution of the fuzzy nonlinear optimization problems (FNLOPs) is gainedusing a projection recurrent neural network (RNN) scheme. Since there is a few research for resolving of FNLOPby RNN's, we establish a new scheme to solve the problem. By reducing theoriginal program to an interval problem and then weighting problem, the Karush--Kuhn--Tucker (KKT)conditions are presented. Moreover, we apply the KKT conditions into a RNN as a efficient tool to solve the problem. Besides, the convergence properties and thestability analysis of the system model are provided. In the final step, several simulation examples are verified to support the obtained results. Reported results are compared with some other previous neural networks.

In this paper, we present some gradient projection algorithms for solving optimization problems with a convex-constrained set. We derive the optimality condition when the convex set is a cone and under some mild assumptions, we prove the convergence of these algorithms. Finally, we apply them to quadratic problems arising in training support vector machines for the Wisconsin Diagnostic Breast Cancer (WDBC) classification problem.

This survey investigates some developments in the second-order characterization of generalized convex functions using the coderivative of subdifferential mapping. More precisely, it presents the second-order characterization for quasiconvex, pseudoconvex and invex functions. Furthermore, it gives some applications of the second-order subdifferentials in optimization problems such as constrained and unconstrained nonlinear programming.

In this paper, we introduce a new iterative algorithm for approximating a common solution of certain class of multiple{sets split variational inequality problems. The sequence of the proposed iterative algorithm is proved to converge strongly in Hilbert spaces. As application, we obtain some strong convergence results for some classes of multiple{sets split convex minimization problems.