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Information Security Game Analysis with Penalty Parameter
2008 International Symposium on Electronic Commerce and Security, 2008This paper analyzes information security in the E-commerce based on game theory, and this game analysis method is applied to information security for the first time. We set up the information security game model of the defender and the attacker, make the equilibrium analysis of this game model, and get the ideal strategy combination.
Wei Sun +3 more
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Smoothing Approximation to the New Exact Penalty Function with Two Parameters
Asia-Pacific Journal of Operational Research, 2021In this paper, we propose a new non-smooth penalty function with two parameters for nonlinear inequality constrained optimization problems. And we propose a twice continuously differentiable function which is smoothing approximation to the non-smooth penalty function and define the corresponding smoothed penalty problem.
Jing Qiu, Jiguo Yu, Shujun Lian
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On the choice of parameters in the method of penalty functions
USSR Computational Mathematics and Mathematical Physics, 1987We consider the following nonlinear programming problem: minimize f(x) subject to \(x\in X=\{x\in E_ n:\) \(g_ i(x)\geq 0\), \(i=1,2,...,m\}\). By means of the modified method of penalty functions this constrained problem is transformed into a sequence of unconstrained problems: minimize \(L_ q(\beta,x)\) subject to \(x\in E_ n\), where \(\beta\to 0 ...
Bereznëv, V. A. +2 more
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A note on the optimum choice for penalty parameters
Communications in Applied Numerical Methods, 1987AbstractThis paper looks at the numerical characteristics of penalty methods for evaluating the solution of symmetric systems of equations with imposed constraints. The sources of error resulting from this approach are identified and an estimate for the penalty parameter that minimizes this error is obtained.
Nour-Omid, Bahram, Wriggers, Peter
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A two parameter mixed interior-exterior penalty algorithm
ZOR Zeitschrift f�r Operations Research Mathematical Methods of Operations Research, 1995Summary: We analyze the mixed penalty methods introduced in the classic book of Fiacco and McCormick using two distinct penalty parameters \(r\), \(t\). The two penalty coefficients induce a two-parameter differentiable trajectory. We analyze the numerical behaviour of an extrapolation strategy that follows the path of the two-parameter trajectory.
Abdelhamid Benchakroun +2 more
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Hyper-heuristics with penalty parameter adaptation for constrained optimization
2014 IEEE Congress on Evolutionary Computation (CEC), 2014Penalty functions are widely used in constrained optimization, but determining optimal penalty parameters or weights turns out to be a difficult optimization problem itself. The paper proposes a hyper-heuristic approach, which searches the optimal penalty weight setting for low-level heuristics, taking the performance of those heuristics with ...
Yu-Jun Zheng 0001 +2 more
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The Choice of a Parameter in a Penalty Method
1982To solve the nonlinear, convex minimization problem min f(x) s. t. g.i(x)≤0, i=l,…,m, we use the SUMT method. We apply the penalty function P(x,r) = f(x) - rΣ log(-g.i(x)). The starting parameter r-┐ is chosen as small as possible, with respect to machine precision for a certain specific problem, so that numerical difficulties (in the sense of ...
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A lower bound for the controlling parameters of the exact penalty functions
Mathematical Programming, 1978The purpose of this paper is to present new exact penalty functions and discuss their properties. A lower bound on the controlling parameters is given, for which above this value, the optimum of the exact penalty function coincides with the optimum of the nonlinear programming problem.
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Information Security Investment Game with Penalty Parameter
2008 3rd International Conference on Innovative Computing Information and Control, 2008The purpose of this paper is to analyze the strategy to promote the information security investment based on game theory. We use game theory to make the analysis and put forward the fruitful strategy suggestions for the defender organization to invest in information security.
Wei Sun +3 more
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Optimal parameter setting of performance based regulation with reward and penalty
2007 IEEE Congress on Evolutionary Computation, 2007The employment of performance based regulation (PBR) in distribution systems could provide some incentive for improving operating efficiency and reducing electricity prices. However, if the PBR mechanism is not properly designed, the enforcement of the PBR may have a negative effect on the supply reliability.
Nuo Xu +3 more
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