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We consider the problem of minimizing a convex objective which is the sum of a smooth part and a non-smooth part. Inspired by various application, we focus on the case when the non-smooth part is a max function. In this paper, we consider to solve such problems using iterative smoothing-gradient methods. We conduct run-time complexity and convergence analysis of smoothing algorithms.
In this paper, we introduce the regularized Newton method for multiobjective optimization. The method does not scalarize the original multiobjective optimization problem. For any vector convex function, with a compact level set, the regularized Newton method generates a sequence that converges to the optimal points from any starting point. Moreover the regularized Newton method does not require strong...
In order to solve the nonlinear programming problem with inequality constraints, a method for smoothing the square-root exact penalty function is proposed. Error estimations are obtained among the optimal objective function values of the smoothed penalty problem, of the nonsmooth exact penalty problem and of the original constrained optimization problem. Based on the smoothed penalty function, an...
Exact penalty function methods for the solution of constrained optimization problem are based on the construction of a function whose unconstrained minimizing points are also solution of the constrained problem. One of the popular exact penalty functions is l1 exact penalty function. However l1 exact penalty function is not a smooth function. In this paper, we propose a new method for smoothing the...
In the resource limited artificial immune system (RLAIS), because the network granularity is determined by the network affinity threshold (NAT) and the initialization value of NAT is obtained by calculating the distance between the antigens each other, the NAT doesn't reflect the network evolution process. The computation of the stimulation level at closer distance doesn't sufficiently reflect its...
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