Abstract
An adaptive projected affine scaling algorithm of cubic regularization method using a filter technique for solving box constrained optimization without derivatives is put forward in the passage. The affine scaling interior-point cubic model is based on the quadratic probabilistic interpolation approach on the objective function. The new iterations are obtained by the solutions of the projected adaptive cubic regularization algorithm with filter technique. We prove the convergence of the proposed algorithm under some assumptions. Finally, experiments results showed that the presented algorithm is effective in detail.
Highlights
In this passage, we investigate the following optimization: minf(y) s.t.y y1, y2, . . . , yn ∈ Rn (1)li ≤ yi ≤ ui i 1, 2, . . . , n, where f: Rn ⟶ R is smooth, but its derivative information is unavailable or unreliable
We review the elements of our presented algorithm
As we all know that the computation of Cauchy condition usually is much cheaper than the computation in Step 3, we will give a relationship between the critical measure κ and the affine gradient. erefore, we can replace the predicted decrease by the Cauchy step at each criticality measure satisfying this relationship
Summary
We investigate the following optimization: minf(y) s.t.y y1, y2, . . . , yn ∈ Rn (1). We investigate the following optimization: minf(y) s.t.y y1, y2, . N, where f: Rn ⟶ R is smooth, but its derivative information is unavailable or unreliable. Li is not greater than ui, and there exists some ik such that lk is less than uk strictly. Define the feasible set and the strict interior by Ω, int(Ω), respectively. E structure of this passage is as shown below. E corresponding analysis are investigated in Sections 3 and 4, respectively.
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