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Accelerating Activation Function for 3- Satisfiability Logic Programming

Mohd Asyraf Mansor, Saratha Sathasivam
2016 International Journal of Intelligent Systems and Applications  
Moreover, evaluations are made between these activation functions to see the robustness via aspects of global solutions, global Hamming distance, and CPU time.  ...  In logic programming, the activation function can be used as a dynamic post optimizat ion paradigm to transform the activation level of a unit (neuron) into an output signal.  ...  Then, the formu la of generating the output can be summarized as follows:       1, 0 1, 0 i i g yx g x x        (10) Hence, if output exceeds the threshold value, the actual state is 1  ... 
doi:10.5815/ijisa.2016.10.05 fatcat:elqhcn7r2jftrow3i44vf27rqy

Boltzmann Machine and Hyperbolic activation function in Higher Order Neuro Symbolic Integration

Muraly Velavan, Zainor Ridzuan bin Yahya, Mohamad Nazri bin Abdul Halif, Saratha Sathasivam
2015 International journal of computational and electronics aspects in engineering  
Hereby we employed Boltzmann Machines and hyperbolic tangent activation function to increased the performance of neuro symbolic integration. We used agent based modelling to model this problem.  ...  Index terms -Boltzmann machine, agent based modelling and hyperbolic tangent activation function I.  ...   Ei=  = n j 1 ujwij -θi (3) Thus,  Ei> 0 means that the energy of the whole system is higher if ui = 0 and higher energy for  Ei< 0 with ui = 1.  ... 
doi:10.26706/ijceae.1.1.20150103 fatcat:6piw6wvbjbapjji2g7rpu4yc7a

Learning Rules Comparison in Neuro-SymbolicIntegration

Saratha Sathasivam
2011 International Journal of Applied Physics and Mathematics  
Comparisons are made between these rules to see which rule is better or outperformed other rules in the aspects of computation time, memory and complexity.  ...  From the computer simulation that has been carried out, the hyperbolic activation function performs better than the other learning methods.  ...  The following Figure 1 shows the global minima ratio (Number of global minima solutions/Number of runs) using hyperbolic activation function approach.  ... 
doi:10.7763/ijapm.2011.v1.25 fatcat:uuhx43izlbcedngvaslomzqw6a

Optimal Implantable Cardioverter Defibrillator (ICD) Generator Replacement

Anahita Khojandi, Lisa M. Maillart, Oleg A. Prokopyev, Mark S. Roberts, Timothy Brown, William W. Barrington
2014 INFORMS journal on computing  
Pardalos, "On Multiple-Ratio Hyperbolic 0-1 Programming Problems," Pacific Journal of Optimization, Vol. 1/2 (2005), pp. 327-345. 39. O.A. Prokopyev, H.-Z. Huang, P.M.  ...  Pardalos, "On Complexity of Unconstrained Hyperbolic 0-1 Programming Problems," Operations Research Letters, Vol. 33/3 (2005), pp. 312-318. 40. H.K. Fung, S. Rao, C.A. Floudas, O.A. Prokopyev, P.M.  ... 
doi:10.1287/ijoc.2013.0586 fatcat:zm5d3gwclre3li7inx3cpqlvam

Page 3677 of Mathematical Reviews Vol. , Issue 84i [page]

1984 Mathematical Reviews  
For many finite programming problems, good globally convergent methods based on the use of exact penalty functions are now available and it is the purpose of this paper to show that precisely analogous  ...  the mixed boundary condition (0/0n)x(t,f)+b({)x(1,$)=f(t,$) in (0, 7] XT.  ... 

Deterministic Global Optimization with Artificial Neural Networks Embedded

Artur M. Schweidtmann, Alexander Mitsos
2018 Journal of Optimization Theory and Applications  
Herein, we present an efficient method for deterministic global optimization of ANN embedded optimization problems.  ...  The optimization problem is solved using our in-house global deterministic solver MAiNGO.  ...  T reactor´3 90˝C ď 0, 360˝C´T reactor ď 0, Q rebC1´1 .97Gcal/h ď 0, 1.31Gcal/h´Q rebC1 ď 0, RR C1´1 ď 0, 0.37´RR C1 ď 0, DF C2´0 .99 ď 0, 0.85´DF C2 ď 0, RR C2´1 .2 ď 0, 0.2´RR C2 ď 0, 0.999´Zprod cum  ... 
doi:10.1007/s10957-018-1396-0 fatcat:u3ymryjhizfrdiqxgn7ossl34m

Boltzmann Machine and Hyperbolic Activation Function in Higher Order Network

Saratha Sathasivam, Muraly Velavan
2014 Modern Applied Science  
The goal is to perform logic programming based on the energy minimization scheme is to achieve the best global minimum. However, there is no guarantee to find the best minimum in the network.  ...  However, by using Boltzmann Machines and hyperbolic tangent activation function this problem can be overcome.  ...  Acknowledgement This research is partly financed by Fundamental Research Grant Scheme (203/ PMATHS/6711368) by Ministry of Higher Education and Universiti Sains Malaysia.  ... 
doi:10.5539/mas.v8n3p140 fatcat:2mtcsjrvsfdpnnbd5o6vpmwbvi

Elliptic and hyperbolic quadratic eigenvalue problems and associated distance problems

Y. Hachez, P. Van Dooren
2003 Linear Algebra and its Applications  
Two important classes of quadratic eigenvalue problems are composed of elliptic and hyperbolic problems.  ...  ., 351-352 (2002) 455], the distance to the nearest non-hyperbolic or non-elliptic quadratic eigenvalue problem is obtained using a global minimization problem.  ...  Acknowledgements The authors discussed the idea of this paper with Yves Genin, Nick Higham, Yurii Nesterov, Françoise Tisseur and Hugo Woerdeman.  ... 
doi:10.1016/s0024-3795(03)00489-0 fatcat:mkrkfjrumvbtjj4tjdhytt27ne

Hyperbolic polynomials [chapter]

2006 Courant Lecture Notes  
Figure 1 : 1 Hyperbolicity cone corresponding to the polynomial p(x, y, z) and is a crucial property in the analysis of the polynomialtime global convergence of Newton's method; see [NN94] or [BV04  ...  A few good references about the use of hyperbolic polynomials in optimization are [Gül97, BGLS01, Ren] .  ... 
doi:10.1090/cln/014/12 fatcat:63qnkl7debg6vbir23lonl5ipm

Certifying polynomial nonnegativity via hyperbolic optimization [article]

James Saunderson
2019 arXiv   pre-print
We describe a new approach to certifying the global nonnegativity of multivariate polynomials by solving hyperbolic optimization problems—a class of convex optimization problems that generalize semidefinite  ...  programs.  ...  thank Amir Ali Ahmadi, Petter Brändén, Hamza Fawzi, Mario Kummer, Simone Naldi, Pablo Parrilo, Levent Tunçel, and Cynthia Vinzant for helpful discussions and correspondence related to various aspects of  ... 
arXiv:1904.00491v2 fatcat:pnsdbncoyzhfjfbxm4pcdxkwri

Toward the development of a Trust-Tech-based methodology for solving mixed integer nonlinear optimization

Bin Wang, Hsiao-Dong Chiang
2011 Nonlinear Theory and Its Applications IEICE  
The Trust-Tech methodology has been developed to solve non-convex global optimization problems [28] [29] [30] and it has been successfully applied to various applications, such as learning finite mixture  ...  Because of the discrete controls involved in power systems, these problems are essentially mixed-integer nonlinear programs.  ...  Such a non-hyperbolic phenomenon is unavoidable because the zero set E F ≡ F −1 (0) = M −1 (0) ∪ H −1 (0) , which is a manifold, usually consists of several path-connected components.  ... 
doi:10.1587/nolta.2.281 fatcat:i6iqtlm3pjekhedxgexs5fnk4u

Page 989 of Mathematical Reviews Vol. 34, Issue 4 [page]

1967 Mathematical Reviews  
a problem of hyperbolic programming.  ...  A method is discussed for evaluating the global minimum of the real-valued function f(z,,---,2z,) on the set K=L,,x---xL,,, where L,, ={0, 1,2, ---,k,;—1} and k,>1 is an integer.  ... 

Continuous Relaxation of MINLP Problems by Penalty Functions: A Practical Comparison [chapter]

M. Fernanda P. Costa, Ana Maria A. C. Rocha, Edite M. G. P. Fernandes
2017 Lecture Notes in Computer Science  
A practical comparison of penalty functions for globally solving mixed-integer nonlinear programming (MINLP) problems is presented.  ...  A new penalty algorithm that addresses simultaneously the reduction of the error tolerances for optimality and feasibility, as well as the reduction of the penalty parameter, is designed.  ...  Data: f * , k max , 0 < ε ≪ 1, 0 < δ ≪ 1, 0 < η ≪ 1, ε 1 > ε, δ 1 > δ, η 1 > η, σ ε ∈ (0, 1), σ δ ∈ (0, 1), σ η ∈ (0, 1); Set k = 1; repeat Compute a δ k -global minimizer x k of problem (3) such that  ... 
doi:10.1007/978-3-319-62398-6_8 fatcat:buecgvrzubazlksksnilpmicuq

Page 8827 of Mathematical Reviews Vol. , Issue 2003k [page]

2003 Mathematical Reviews  
[Ahmed, Shabbir] (1-GAIT-I; Atlanta, GA); Sahinidis, Nikolaos V. (1-IL-KE; Urbana, IL) Global optimization of 0-1 hyperbolic programs. (English summary) J. Global Optim. 24 (2002), no. 4, 385-416.  ...  Summary: “We develop eight different mixed-integer convex pro- gramming reformulations of 0-1 hyperbolic programs.  ... 

Symbolic computation in hyperbolic programming

Simone Naldi, Daniel Plaumann
2017 Journal of Algebra and its Applications  
Hyperbolic programming is the problem of computing the infimum of a linear function when restricted to the hyperbolicity cone of a hyperbolic polynomial, a generalization of semidefinite programming.  ...  This allows us to design exact algorithms able to certify the multiplicity of the solution and the optimal value of the linear function.  ...  Hyperbolic programming Hyperbolic programming is a convex optimization problem specified as follows.  ... 
doi:10.1142/s021949881850192x fatcat:j7a3xhva2bcwhfamm4smufw25a
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