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ShuvomoyShuvomoy
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Updated the tutorial files
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‎examples/tutorials/accelerated_gradient_strongly_convex.tutorial.ipynb‎

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@@ -12,7 +12,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"execution_count": 13,
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"metadata": {},
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"outputs": [],
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"source": [
@@ -28,7 +28,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {},
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"outputs": [
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{
@@ -37,7 +37,7 @@
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"PEP(AbstractFunction[], Point[], Constraint[], Expression[], PSDMatrix[], nothing)"
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]
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},
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"execution_count": 2,
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"execution_count": 14,
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"metadata": {},
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"output_type": "execute_result"
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}
@@ -54,12 +54,12 @@
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"\n",
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"Consider the convex minimization problem\n",
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"$$f_\\star \\triangleq \\min_x f(x),$$\n",
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"where $f$ is $L$-smooth and $\\mu$-strongly convex. For this example, let us take $\\mu=0.1$ and $L=1$. Let us declare this function type in `PEPit`. "
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"where $f$ is $L$-smooth and $\\mu$-strongly convex. For this example, let us take $\\mu=0.1$ and $L=1$. Let us declare this function type in `PEPit` next. Let us start with defining the parameters $\\mu$ and $L$. "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"execution_count": 15,
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"metadata": {},
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"outputs": [
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{
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" \"L\" => 1"
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]
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},
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"execution_count": 3,
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"execution_count": 15,
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"metadata": {},
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"output_type": "execute_result"
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}
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"execution_count": 16,
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"metadata": {},
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"outputs": [
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{
@@ -99,7 +99,7 @@
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"SmoothStronglyConvexFunction(0.1, 1.0, PEPFunction(1, true, OrderedDict{PEPFunction, Float64}(PEPFunction(\u001b[33m#= circular reference @-2 =#\u001b[39m) => 1.0), true, Tuple{Point, Point, Expression}[], Tuple{Point, Point, Expression}[], Constraint[], PSDMatrix[], PSDMatrix[], 0))"
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]
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},
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"execution_count": 4,
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"execution_count": 16,
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"metadata": {},
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"output_type": "execute_result"
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}
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"metadata": {},
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"outputs": [
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{
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"2"
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]
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},
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"execution_count": 5,
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"execution_count": 17,
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"metadata": {},
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"output_type": "execute_result"
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}
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},
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"cell_type": "code",
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"execution_count": 18,
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"metadata": {},
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"outputs": [
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{
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"Point(5, true, OrderedDict{Point, Float64}(Point(\u001b[33m#= circular reference @-2 =#\u001b[39m) => 1.0), 1, nothing)"
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]
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},
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"execution_count": 6,
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"output_type": "execute_result"
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}
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},
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"cell_type": "code",
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"metadata": {},
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{
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" Constraint(Expression(15, false, OrderedDict{Any, Float64}(Expression(6, true, OrderedDict{Any, Float64}(Expression(\u001b[33m#= circular reference @-2 =#\u001b[39m) => 1.0), 1, nothing) => 1.0, Expression(4, true, OrderedDict{Any, Float64}(Expression(\u001b[33m#= circular reference @-2 =#\u001b[39m) => 1.0), 0, nothing) => -1.0, (Point(5, true, OrderedDict{Point, Float64}(Point(\u001b[33m#= circular reference @-2 =#\u001b[39m) => 1.0), 1, nothing), Point(5, true, OrderedDict{Point, Float64}(Point(\u001b[33m#= circular reference @-2 =#\u001b[39m) => 1.0), 1, nothing)) => 0.05, (Point(5, true, OrderedDict{Point, Float64}(Point(\u001b[33m#= circular reference @-2 =#\u001b[39m) => 1.0), 1, nothing), Point(2, true, OrderedDict{Point, Float64}(Point(\u001b[33m#= circular reference @-2 =#\u001b[39m) => 1.0), 0, nothing)) => -0.05, (Point(2, true, OrderedDict{Point, Float64}(Point(\u001b[33m#= circular reference @-2 =#\u001b[39m) => 1.0), 0, nothing), Point(5, true, OrderedDict{Point, Float64}(Point(\u001b[33m#= circular reference @-2 =#\u001b[39m) => 1.0), 1, nothing)) => -0.05, (Point(2, true, OrderedDict{Point, Float64}(Point(\u001b[33m#= circular reference @-2 =#\u001b[39m) => 1.0), 0, nothing), Point(2, true, OrderedDict{Point, Float64}(Point(\u001b[33m#= circular reference @-2 =#\u001b[39m) => 1.0), 0, nothing)) => 0.05, 1 => -1.0), nothing, nothing), \"inequality\", 0, nothing, nothing)"
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"Expression(32, true, OrderedDict{Any, Float64}(Expression(\u001b[33m#= circular reference @-2 =#\u001b[39m) => 1.0), 3, nothing)"
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" Expression(35, false, OrderedDict{Any, Float64}(Expression(32, true, OrderedDict{Any, Float64}(Expression(\u001b[33m#= circular reference @-2 =#\u001b[39m) => 1.0), 3, nothing) => 1.0, Expression(4, true, OrderedDict{Any, Float64}(Expression(\u001b[33m#= circular reference @-2 =#\u001b[39m) => 1.0), 0, nothing) => -1.0), nothing, nothing)"
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},
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"0.34760221803672986"
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]
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"cell_type": "markdown",
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"source": [
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"We should see the output:\n",
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"\n",
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"````Julia\n",
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"PEPit guarantee: f(x_n)-f_* <= 0.347602 (f(x_0) - f(x_*) + mu/2*||x_0 - x_*||^2)\n",
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"\n",
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"Theoretical guarantee: f(x_n)-f_* <= 0.467544 (f(x_0) - f(x_*) + mu/2*||x_0 - x_*||^2)\n",
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"````\n",
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"\n",
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"So the gurantee that we found via `PEPit` is tighter than the theoretical guarantee!\n",
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"\n",
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"**References**:\n",
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Julia 1.12",
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"display_name": "Julia 1.12.2",
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"language": "julia",
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"name": "julia-1.12"
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},

‎examples/tutorials/accelerated_gradient_strongly_convex.tutorial.jl‎

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Original file line numberDiff line numberDiff line change
@@ -23,7 +23,7 @@ problem = PEP()
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Consider the convex minimization problem
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$$f_\star \triangleq \min_x f(x),$$
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where $f$ is $L$-smooth and $\mu$-strongly convex. For this example, let us take $\mu=0.1$ and $L=1$. Let us declare this function type in `PEPit`.
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where $f$ is $L$-smooth and $\mu$-strongly convex. For this example, let us take $\mu=0.1$ and $L=1$. Let us declare this function type in `PEPit` next. Let us start with defining the parameters $\mu$ and $L$.
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=#
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#=
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We should see the output:
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````Julia
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PEPit guarantee: f(x_n)-f_* <= 0.347602 (f(x_0) - f(x_*) + mu/2*||x_0 - x_*||^2)
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Theoretical guarantee: f(x_n)-f_* <= 0.467544 (f(x_0) - f(x_*) + mu/2*||x_0 - x_*||^2)
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````
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So the gurantee that we found via `PEPit` is tighter than the theoretical guarantee!
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**References**:

‎examples/tutorials/accelerated_gradient_strongly_convex.tutorial.md‎

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Original file line numberDiff line numberDiff line change
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Consider the convex minimization problem
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$$f_\star \triangleq \min_x f(x),$$
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where $f$ is $L$-smooth and $\mu$-strongly convex. For this example, let us take $\mu=0.1$ and $L=1$. Let us declare this function type in `PEPit`.
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where $f$ is $L$-smooth and $\mu$-strongly convex. For this example, let us take $\mu=0.1$ and $L=1$. Let us declare this function type in `PEPit` next. Let us start with defining the parameters $\mu$ and $L$.
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````julia
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@info "📝 Theoretical guarantee: f(x_n)-f_* <= $(round(τ_Theory, digits=6)) (f(x_0) - f(x_*) + mu/2*||x_0 - x_*||^2)"
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````
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We should see the output:
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````Julia
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PEPit guarantee: f(x_n)-f_* <= 0.347602 (f(x_0) - f(x_*) + mu/2*||x_0 - x_*||^2)
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Theoretical guarantee: f(x_n)-f_* <= 0.467544 (f(x_0) - f(x_*) + mu/2*||x_0 - x_*||^2)
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````
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So the gurantee that we found via `PEPit` is tighter than the theoretical guarantee!
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**References**:

‎examples/tutorials/accelerated_gradient_strongly_convex.tutorial.pdf‎

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‎examples/tutorials/accelerated_gradient_strongly_convex.tutorial.tex‎

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\begin{equation*}
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f_\star \triangleq \min_x f(x),
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\end{equation*}
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where $f$ is $L$-smooth and $\mu$-strongly convex. For this example, let us take $\mu=0.1$ and $L=1$. Let us declare this function type in \texttt{PEPit}.
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where $f$ is $L$-smooth and $\mu$-strongly convex. For this example, let us take $\mu=0.1$ and $L=1$. Let us declare this function type in \texttt{PEPit} next. Let us start with defining the parameters $\mu$ and $L$.
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\begin{tcblisting}{listing only, minted language=julia, minted options={mathescape=true, breaklines}, colback=lightgray, colframe=black, boxrule=0pt, toprule=2pt, bottomrule=2pt, arc=0pt, outer arc=0pt, left=5pt, right=5pt, top=5pt, bottom=5pt}
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\end{tcblisting}
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We should see the output:
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\begin{tcblisting}{listing only, minted language=julia, minted options={mathescape=true, breaklines}, colback=lightgray, colframe=black, boxrule=0pt, toprule=2pt, bottomrule=2pt, arc=0pt, outer arc=0pt, left=5pt, right=5pt, top=5pt, bottom=5pt}
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PEPit guarantee: f(x_n)-f_* <= 0.347602 (f(x_0) - f(x_*) + mu/2*||x_0 - x_*||^2)
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Theoretical guarantee: f(x_n)-f_* <= 0.467544 (f(x_0) - f(x_*) + mu/2*||x_0 - x_*||^2)
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\end{tcblisting}
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So the gurantee that we found via \texttt{PEPit} is tighter than the theoretical guarantee!
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\textbf{References}:

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