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In this paper, a new filled function method for finding a global minimizer of global optimization is proposed. The proposed filled function is continuously differentiable and only contains one parameter. It has no parameter sensitive terms. As a result, a general classical local optimization method can be used to find a better minimizer of the proposed filled function with easy parameter adjustment. Numerical experiments show that the proposed filled function method is effective.  相似文献
2.
The incompressible Boussinesq equations not only have many applications in modeling fluids and geophysical fluids but also are mathematically important. The well-posedness and related problem on the Boussinesq equations have recently attracted considerable interest. This paper examines the global regularity issue on the 2D Boussinesq equations with fractional Laplacian dissipation and thermal diffusion. Attention is focused on the case when the thermal diffusion dominates. We establish the global well-posedness for the 2D Boussinesq equations with a new range of fractional powers of the Laplacian.  相似文献
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We consider the n-dimensional modified quasi-geostrophic (SQG) equations
tθ + u . ∇θ + κΛαθ = 0,$∂tθ + u . ∇θ + κΛαθ = 0,$
u = Λα-1 Rθ$u = Λα-1 R⊥θ$
with κ > 0, α ∈ (0,1] and θ0W1, ∞ (?n). In this paper, we establish a different proof for the global regularity of this system. The original proof was given by Constantin, Iyer, and Wu , who employed the approach of Besov space techniques to study the global existence and regularity of strong solutions to modified critical SQG equations for two dimensional case. The proof provided in this paper is based on the nonlinear maximum principle as well as the approach in Constantin and Vicol .  相似文献
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In this work, the process of distribution functions of a one-dimensional super-Lévy process with general branching mechanism is characterized as the pathwise unique solution of a stochastic integral equation driven by time–space Gaussian white noises and Poisson random measures. This generalizes the recent work of Xiong (2013), where the result for a super-Brownian motion with binary branching mechanism was obtained.  相似文献
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In this note, we consider the optimality criteria of multi-objective programming problems without constraint qualifications involving generalized convexity. Under the E-pseudoconvexity assumptions, the unified necessary and sufficient optimality conditions are established for weakly efficient and efficient solutions, respectively, in multi-objective programming problems.  相似文献
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