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‎404.html‎

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<!doctype html> <html lang=en > <meta charset=UTF-8 > <meta name=viewport content="width=device-width, initial-scale=1"> <link rel=stylesheet href="/blogs/css/franklin.css"> <link rel=stylesheet href="/blogs/css/tufte.css"> <link rel=stylesheet href="/blogs/css/latex.css"> <link rel=stylesheet href="/blogs/css/adjust.css"> <link rel=stylesheet href="/blogs/css/FranklinTheorems.css"> <link rel=icon href="/blogs/assets/favicon.png"> <title>Blogs by Shuvomoy Das Gupta</title> <link rel=icon href="/blogs/assets/favicon.ico"> <script src="/blogs/libs/lunr/lunr.min.js"></script> <script src="/blogs/libs/lunr/lunr_index.js"></script> <script src="/blogs/libs/lunr/lunrclient.min.js"></script> <div id=layout > <div id=menu > <ul> <li><a href="/blogs/">Blogs</a> <li><a href="/blogs/index.html#tags">Tags</a> <li><a href="https://shuvomoy.github.io/">Website</a> <li><form id=lunrSearchForm name=lunrSearchForm > <input class=search-input name=q placeholder=" " type=text > <input type=submit value=Search formaction="/blogs/search/index.html"> </form> </ul> </div> <div id=main > <!-- Content appended here .result-title a { text-decoration: none; } .result-title a:hover { text-decoration: underline; } .result-preview { color: #808080; } .resultCount { color: #808080; } .result-query { font-weight: bold; } #lunrSearchForm { margin-top: 1em; } --> <div class=franklin-content ><h1 id=blogs_by_shuvomoy_das_gupta ><a href="#blogs_by_shuvomoy_das_gupta" class=header-anchor >Blogs by Shuvomoy Das Gupta</a></h1> <h2 id=404_file_not_found ><a href="#404_file_not_found" class=header-anchor >404: File not found</a></h2> <p>I have recently moved my blogs to a <a href="https://franklinjl.org/"><code>Franklin.jl</code></a> based website, so the previous blog urls may not work. Almost all my previous blogs are available at <a href="https://shuvomoy.github.io/blogs/">https://shuvomoy.github.io/blogs/</a>.</p> <div class=page-foot > <div class=copyright > &copy; Shuvomoy Das Gupta. Last modified: April 15, 2025. Website built with <a href="https://github.com/tlienart/Franklin.jl">Franklin.jl</a> and the <a href="https://julialang.org">Julia programming language</a>. </div> </div> </div> </div> </div>
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<!doctype html> <html lang=en > <meta charset=UTF-8 > <meta name=viewport content="width=device-width, initial-scale=1"> <link rel=stylesheet href="/blogs/css/franklin.css"> <link rel=stylesheet href="/blogs/css/tufte.css"> <link rel=stylesheet href="/blogs/css/latex.css"> <link rel=stylesheet href="/blogs/css/adjust.css"> <link rel=stylesheet href="/blogs/css/FranklinTheorems.css"> <link rel=icon href="/blogs/assets/favicon.png"> <title>Blogs by Shuvomoy Das Gupta</title> <link rel=icon href="/blogs/assets/favicon.ico"> <script src="/blogs/libs/lunr/lunr.min.js"></script> <script src="/blogs/libs/lunr/lunr_index.js"></script> <script src="/blogs/libs/lunr/lunrclient.min.js"></script> <div id=layout > <div id=menu > <ul> <li><a href="/blogs/">Blogs</a> <li><a href="/blogs/index.html#tags">Tags</a> <li><a href="https://shuvomoy.github.io/">Website</a> <li><form id=lunrSearchForm name=lunrSearchForm > <input class=search-input name=q placeholder=" " type=text > <input type=submit value=Search formaction="/blogs/search/index.html"> </form> </ul> </div> <div id=main > <!-- Content appended here .result-title a { text-decoration: none; } .result-title a:hover { text-decoration: underline; } .result-preview { color: #808080; } .resultCount { color: #808080; } .result-query { font-weight: bold; } #lunrSearchForm { margin-top: 1em; } --> <div class=franklin-content ><h1 id=blogs_by_shuvomoy_das_gupta ><a href="#blogs_by_shuvomoy_das_gupta" class=header-anchor >Blogs by Shuvomoy Das Gupta</a></h1> <h2 id=404_file_not_found ><a href="#404_file_not_found" class=header-anchor >404: File not found</a></h2> <p>I have recently moved my blogs to a <a href="https://franklinjl.org/"><code>Franklin.jl</code></a> based website, so the previous blog urls may not work. Almost all my previous blogs are available at <a href="https://shuvomoy.github.io/blogs/">https://shuvomoy.github.io/blogs/</a>.</p> <div class=page-foot > <div class=copyright > &copy; Shuvomoy Das Gupta. Last modified: April 21, 2025. Website built with <a href="https://github.com/tlienart/Franklin.jl">Franklin.jl</a> and the <a href="https://julialang.org">Julia programming language</a>. </div> </div> </div> </div> </div>

‎index.html‎

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‎posts/A-lower-complexity-bound-for-the-class-of-convex-and-Lipschitz-continuous-functions/index.html‎

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‎posts/Accelerated_methods_as_span_based_first_order_method/index.html‎

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\*SubscriptBox&#91;\&#40;g\&#41;, \&#40;j\&#41;&#93;\ \&#40;&#40;\&#40;-
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j\&#41;&#93;&#41;\&#41;\&#41;, \&#40;L\&#41;&#93;\&#41;&#41;/Subscript&#91;\&#91;Theta&#93;, 1&#43;i&#93;*&#41;</code></pre> \[\begin{align*} x_{i+1} & =x_{i}-\frac{\left(\theta_{i}-1\right)}{\theta_{i+1}}\sum_{j=0}^{i-2}\frac{\left(h_{i,j}-h_{i-1,j}\right)}{L}g_{j}\\ & -\frac{\left(\theta_{i}-1\right)\left(h_{i,i-1}-1\right)}{L\theta_{i+1}}g_{i-1}-\frac{\left(2\theta_{i}+\theta_{i+1}-1\right)}{L\theta_{i+1}}g_{i}.\quad(\textrm{SBFOM-OGM})\end{align*}\] <p>​ Recall that, using &#40;2&#41; any &#40;SBFOM&#41; satisfying sequence will obey: </p> \[x_{i+1}=x_{i}-\sum_{j=0}^{i-1}\frac{(h_{i+1,j}-h_{i,j})}{L}g_{j}-\frac{h_{i+1,i}}{L}g_{i}\quad(3)\] <p>​ Note that &#40;3&#41; and &#40;SBFOM-OGM&#41; are in the same format now for a pattern matching. Comparing the terms part by part, we get the following recursive system: </p> \[\begin{align*} \forall_{j\in[0:i-2]}\quad h_{i+1,j} & -h_{i,j}=\frac{\left(\theta_{i}-1\right)}{\theta_{i+1}}\left(h_{i,j}-h_{i-1,j}\right)\\ h_{i+1,i-1}-h_{i,i-1} & =\frac{\left(\theta_{i}-1\right)\left(h_{i,i-1}-1\right)}{\theta_{i+1}}\\ h_{i+1,i} & =\frac{\left(2\theta_{i}+\theta_{i+1}-1\right)}{\theta_{i+1}},\end{align*}\] <p>​ with initial condition \(h_{1,j}=0\)​ for \(j<0\)​ and \(h_{0,j}=0\)​ for all \(j\)​.</p> <div class=page-foot > <div class=copyright > &copy; Shuvomoy Das Gupta. Last modified: April 15, 2025. Website built with <a href="https://github.com/tlienart/Franklin.jl">Franklin.jl</a> and the <a href="https://julialang.org">Julia programming language</a>. </div> </div> </div> </div> </div> <script src="/blogs/libs/katex/katex.min.js"></script> <script src="/blogs/libs/katex/auto-render.min.js"></script> <script>renderMathInElement(document.body)</script> <script src="/blogs/libs/highlight/highlight.pack.js"></script> <script>hljs.initHighlightingOnLoad();hljs.configure({tabReplace: ' '});</script>
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j\&#41;&#93;&#41;\&#41;\&#41;, \&#40;L\&#41;&#93;\&#41;&#41;/Subscript&#91;\&#91;Theta&#93;, 1&#43;i&#93;*&#41;</code></pre> \[\begin{align*} x_{i+1} & =x_{i}-\frac{\left(\theta_{i}-1\right)}{\theta_{i+1}}\sum_{j=0}^{i-2}\frac{\left(h_{i,j}-h_{i-1,j}\right)}{L}g_{j}\\ & -\frac{\left(\theta_{i}-1\right)\left(h_{i,i-1}-1\right)}{L\theta_{i+1}}g_{i-1}-\frac{\left(2\theta_{i}+\theta_{i+1}-1\right)}{L\theta_{i+1}}g_{i}.\quad(\textrm{SBFOM-OGM})\end{align*}\] <p>​ Recall that, using &#40;2&#41; any &#40;SBFOM&#41; satisfying sequence will obey: </p> \[x_{i+1}=x_{i}-\sum_{j=0}^{i-1}\frac{(h_{i+1,j}-h_{i,j})}{L}g_{j}-\frac{h_{i+1,i}}{L}g_{i}\quad(3)\] <p>​ Note that &#40;3&#41; and &#40;SBFOM-OGM&#41; are in the same format now for a pattern matching. Comparing the terms part by part, we get the following recursive system: </p> \[\begin{align*} \forall_{j\in[0:i-2]}\quad h_{i+1,j} & -h_{i,j}=\frac{\left(\theta_{i}-1\right)}{\theta_{i+1}}\left(h_{i,j}-h_{i-1,j}\right)\\ h_{i+1,i-1}-h_{i,i-1} & =\frac{\left(\theta_{i}-1\right)\left(h_{i,i-1}-1\right)}{\theta_{i+1}}\\ h_{i+1,i} & =\frac{\left(2\theta_{i}+\theta_{i+1}-1\right)}{\theta_{i+1}},\end{align*}\] <p>​ with initial condition \(h_{1,j}=0\)​ for \(j<0\)​ and \(h_{0,j}=0\)​ for all \(j\)​.</p> <div class=page-foot > <div class=copyright > &copy; Shuvomoy Das Gupta. Last modified: April 21, 2025. Website built with <a href="https://github.com/tlienart/Franklin.jl">Franklin.jl</a> and the <a href="https://julialang.org">Julia programming language</a>. </div> </div> </div> </div> </div> <script src="/blogs/libs/katex/katex.min.js"></script> <script src="/blogs/libs/katex/auto-render.min.js"></script> <script>renderMathInElement(document.body)</script> <script src="/blogs/libs/highlight/highlight.pack.js"></script> <script>hljs.initHighlightingOnLoad();hljs.configure({tabReplace: ' '});</script>

‎posts/An-improved-lower-complexity-bound-for-the-class-of-convex-and-Lipschitz-continuous-functions/index.html‎

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‎posts/An-understanding-by-Tagore/index.html‎

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‎posts/Automatic_sdp_relaxation_of_QCQP_in_JuMP_Julia/index.html‎

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<pre><code class="julia hljs">x_star_SDP, y_star_SDP, Z_star_SDP, W_star_SDP, p_star_SDP = SDP_relaxation_solver(c_1, c_2, c_3, a_1, x_lb, x_ub, y_lb, y_ub, QuadCon1StdTerms, QuadCon2StdTerms; big_M = <span class=hljs-number >100</span>, RLT_cut = :on)</code></pre>
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&copy; Shuvomoy Das Gupta. Last modified: April 15, 2025. Website built with <a href="https://github.com/tlienart/Franklin.jl">Franklin.jl</a> and the <a href="https://julialang.org">Julia programming language</a>.
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&copy; Shuvomoy Das Gupta. Last modified: April 21, 2025. Website built with <a href="https://github.com/tlienart/Franklin.jl">Franklin.jl</a> and the <a href="https://julialang.org">Julia programming language</a>.
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‎posts/Computing-composition-of-operators-via-scaled-relative-graph-in-Mathematica/index.html‎

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&copy; Shuvomoy Das Gupta. Last modified: April 15, 2025. Website built with <a href="https://github.com/tlienart/Franklin.jl">Franklin.jl</a> and the <a href="https://julialang.org">Julia programming language</a>.
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&copy; Shuvomoy Das Gupta. Last modified: April 21, 2025. Website built with <a href="https://github.com/tlienart/Franklin.jl">Franklin.jl</a> and the <a href="https://julialang.org">Julia programming language</a>.
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‎posts/Computing-proximal-operator-of-a-constrained-function-in-Julia/index.html‎

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X_sol = JuMP.value.(X_tl)</code></pre> <h6 id=converting_jmd_file_to_jl_file ><a href="#converting_jmd_file_to_jl_file" class=header-anchor >Converting <code>.jmd</code> file to <code>.jl</code> file</a></h6> <p>To convert the <code>.jmd</code> file to a <code>.jl</code> file we run the following code:</p> <pre><code class="julia hljs"><span class=hljs-keyword >using</span> Weave
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cd(<span class=hljs-string >&quot;C:\\Users\\shuvo\\Google Drive\\GitHub\\blog\\codes&quot;</span>) <span class=hljs-comment ># directory that contains the .jmd file</span>
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tangle(<span class=hljs-string >&quot;2020-09-08-proximal_operator_over_matrix.jmd&quot;</span>, informat = <span class=hljs-string >&quot;markdown&quot;</span>) <span class=hljs-comment ># convert the .jmd file into a .jl file that will contain the code</span></code></pre> <div class=page-foot > <div class=copyright > &copy; Shuvomoy Das Gupta. Last modified: April 15, 2025. Website built with <a href="https://github.com/tlienart/Franklin.jl">Franklin.jl</a> and the <a href="https://julialang.org">Julia programming language</a>. </div> </div> </div> </div> </div>
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tangle(<span class=hljs-string >&quot;2020-09-08-proximal_operator_over_matrix.jmd&quot;</span>, informat = <span class=hljs-string >&quot;markdown&quot;</span>) <span class=hljs-comment ># convert the .jmd file into a .jl file that will contain the code</span></code></pre> <div class=page-foot > <div class=copyright > &copy; Shuvomoy Das Gupta. Last modified: April 21, 2025. Website built with <a href="https://github.com/tlienart/Franklin.jl">Franklin.jl</a> and the <a href="https://julialang.org">Julia programming language</a>. </div> </div> </div> </div> </div>

‎posts/Constructing-an-interpolated-function-for-the-class-of-smooth-convex-functions/index.html‎

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