quadprog optimization solver (MathWorks Inc)
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Quadprog Optimization Solver, supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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Due to the linearity of E ∃( i , ω , a , b ) in a and b , the cost function in (11a) is a quadratic function of the coefficient vector [ b T , a T ] T , which can be reformulated as 12a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{1}{2}[{{\varvec{b}}^{\text{T}}},{{\varvec{a}}^{\text{T}}}]{\varvec{P}}\left[ {\begin{array}{*{20}{c}} {\varvec{b}} \\ {\varvec{a}} \end{array}} \right]+{{\varvec{q}}^{\text{T}}}\left[ {\begin{array}{*{20}{c}} {\varvec{b}} \\ {\varvec{a}} \end{array}} \right]+{\text{constant}}$$\end{document} with 12b \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{P}} = \sum\limits_{{\omega \in {{\bar {\varOmega }}_{\text{p}}} \cup {{\bar {\varOmega }}_{\text{s}}}}} {2\bar {W}(\omega ,{\varvec{a}}(i))\operatorname{Re} \left[ {\phi (\omega )\phi {{( - \omega )}^{\text{T}}}} \right]} ,$$\end{document} 12c \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{q}} = - \sum\limits_{{\omega \in {{\bar {\varOmega }}_{\text{p}}} \cup {{\bar {\varOmega }}_{\text{s}}}}} {2\bar {W}(\omega ,{\varvec{a}}(i))\operatorname{Re} [D(\omega )\phi (\omega )]} ,$$\end{document} 12d \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi (\omega ) = {[1,{{\text{e}}^{ - {\text{j}}\omega }}, \ldots ,{{\text{e}}^{ - {\text{j}}M\omega }}, - D(\omega )[{{\text{e}}^{ - {\text{j}}\omega }}, \ldots ,{{\text{e}}^{ - {\text{j}}N\omega }}]]^{\text{T}}}.$$\end{document} Then, the constrained WLS problem (11) is equivalent to a quadratic programming that can be well solved by the function “quadprog” in the |
