In this paper, a generalized Hoppeld model with continuous neurons using Lagrange multipliers, originally introduced in 12], is thoroughly analysed. We have termed the model the Hoppeld-Lagrange model. It can be used to resolve constrained optimization problems. In the theoretical part, we present a simple explanation of a fundamental energy term of the continuous Hoppeld model. This term has c...

Chaotic simulated annealing (CSA) proposed by Chen and Aihara has been successfully used to solve a variety of combinatorial optimization problems. CSA uses a penalty term to enforce solution validity as in the original Hopfield-Tank approach. There exists a conflict between solution quality and solution validity in the penalty approach. It is often difficult to adjust the relative magnitude of...

A three-level domain decomposition is considered. Bodies in contact with each other are divided into subdomains, which in turn are the union of elements. Using an approach based purely on FETI (finite element tearing and interconnecting) algorithms with only Lagrange multipliers as unknowns, which has been developed by the engineering community, does not lead to a scalable algorithm with respec...

One important issue in the theory of Ordered Weighted Averaging (OWA) operators is the determination of the associated weights. One of the first approaches, suggested by O’Hagan, determines a special class of OWA operators having maximal Shannon entropy of the OWA weights for a given level of orness; algorithmically it is based on the solution of a constrained optimization problem. In this pape...

The current paper has presented the study on theoretical dependences of optimization parameter (the degree transmission transparency) design factors elastic-damping mechanism (EDM) in for tractors small traction class (14 kN). purpose was to obtain a unified functional relationship that integrates early results. determination function based reaching compromise by method indefinite Lagrange mult...

In this study, the finite element model updating was simulated by reducing the stiffness of the members. Due to lack of access to the experimental results, the data obtained from an analytical model were used in the proposed structural damage scenarios. The updating parameters for the studied structures were defined as a reduction coefficient applied to the stiffness of the members. Parameter v...

Fuzzy entropy clustering is an improved fuzzy C-means algorithm and is proposed in the past years. In this paper, by introducing the generalized entropy into fuzzy clustering, we obtain the objective function of the generalized entropy, and use neural networks and the augmented Lagrange method to solve the optimization problem with objective function of generalized entropy. Afterwards, we prese...

In this brief, kernel principal component analysis (KPCA) is reinterpreted as the solution to a convex optimization problem. Actually, there is a constrained convex problem for each principal component, so that the constraints guarantee that the principal component is indeed a solution, and not a mere saddle point. Although these insights do not imply any algorithmic improvement, they can be us...

We introduce an alternative to the smoothing technique approach for constrained optimization. As it turns out for any given smoothing function there exists a modification with particular properties. We use the modification for Nonlinear Rescaling (NR) the constraints of a given constrained optimization problem into an equivalent set of constraints. The constraints transformation is scaled by a ...