Graduate Seminar Report On Non Commutative Noetherian Rings

III this project a derivative-free (DF) surrogate-based trust regiollrnoptimization approach is proposed. In the proposed approach, quadraticrnsurrogate models are constructed and successively IIpdated. The generatedrnsurrogate model is then optimized instead oj the underlined objectivernj unction over trust regions. Trullcated conjugate gradients are employed tornfind the optimal point within each trust region. The approach COl/structs therninitial quadratic surrogate model using few data points oj order 0(11), wherernII is the lIumber oj design variables. The proposed approach adoptsrnweighted least squares fitting Jar updatillg the SlIrrogate model illstead ojrninterpolation which ;s commollly used ill DF optimization, This makes thernapproach more suitable/or s tochastic optim ization and for funcliolls subjectrn[0 I/Il1llerical error. The weights are assigl/ed 10 give more emphasis tornpoints close to th e current center point.

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