From f8446d9249b9eee43b7360c3550d4e6b985d7593 Mon Sep 17 00:00:00 2001
From: FBumann <117816358+FBumann@users.noreply.github.com>
Date: Mon, 11 May 2026 15:09:55 +0200
Subject: [PATCH 1/2] docs: silence HiGHS console output in tutorial notebooks

HiGHS prints a banner + progress lines to the Python REPL on every
m.solve() call by default.  In a tutorial that calls solve many times,
this drowns the actual lesson in solver chatter.  Pass output_flag=False
(a HiGHS solver option forwarded via **solver_options) to suppress it.

Touches the four notebooks where solver_name="highs" is the only solver
invoked:

- create-a-model.ipynb
- create-a-model-with-coordinates.ipynb
- manipulating-models.ipynb (9 solves)
- transport-tutorial.ipynb

Left alone:
- infeasible-model.ipynb (uses Gurobi, kwarg is OutputFlag there;
  also showing solver feedback may be pedagogically relevant for
  infeasibility detection).
- solve-on-remote.ipynb / solve-on-oetc.ipynb (remote handler manages
  its own logging).
- piecewise-*.ipynb (already addressed in #677).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
---
 examples/create-a-model-with-coordinates.ipynb |  2 +-
 examples/create-a-model.ipynb                  |  2 +-
 examples/manipulating-models.ipynb             | 18 +++++++++---------
 examples/transport-tutorial.ipynb              |  2 +-
 4 files changed, 12 insertions(+), 12 deletions(-)

diff --git a/examples/create-a-model-with-coordinates.ipynb b/examples/create-a-model-with-coordinates.ipynb
index f2b12eed..e84c21b9 100644
--- a/examples/create-a-model-with-coordinates.ipynb
+++ b/examples/create-a-model-with-coordinates.ipynb
@@ -150,7 +150,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "m.solve(solver_name=\"highs\")"
+    "m.solve(solver_name=\"highs\", output_flag=False)"
    ]
   },
   {
diff --git a/examples/create-a-model.ipynb b/examples/create-a-model.ipynb
index a158e0cf..b6fc9705 100644
--- a/examples/create-a-model.ipynb
+++ b/examples/create-a-model.ipynb
@@ -215,7 +215,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "m.solve(solver_name=\"highs\")"
+    "m.solve(solver_name=\"highs\", output_flag=False)"
    ]
   },
   {
diff --git a/examples/manipulating-models.ipynb b/examples/manipulating-models.ipynb
index 81106ab3..6903386b 100644
--- a/examples/manipulating-models.ipynb
+++ b/examples/manipulating-models.ipynb
@@ -48,9 +48,9 @@
     "con2 = m.add_constraints(5 * x + 2 * y >= 3 * factor, name=\"con2\")\n",
     "\n",
     "m.add_objective(x + 2 * y)\n",
-    "m.solve(solver_name=\"highs\")\n",
+    "m.solve(solver_name=\"highs\", output_flag=False)\n",
     "\n",
-    "m.solve(solver_name=\"highs\")\n",
+    "m.solve(solver_name=\"highs\", output_flag=False)\n",
     "sol = m.solution.to_dataframe()\n",
     "sol.plot(grid=True, ylabel=\"Optimal Value\")"
    ]
@@ -95,7 +95,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "m.solve(solver_name=\"highs\")\n",
+    "m.solve(solver_name=\"highs\", output_flag=False)\n",
     "sol = m.solution.to_dataframe()\n",
     "sol.plot(grid=True, ylabel=\"Optimal Value\")"
    ]
@@ -137,7 +137,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "m.solve(solver_name=\"highs\")\n",
+    "m.solve(solver_name=\"highs\", output_flag=False)\n",
     "sol = m.solution.to_dataframe()\n",
     "sol.plot(grid=True, ylabel=\"Optimal Value\")"
    ]
@@ -190,7 +190,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "m.solve(solver_name=\"highs\")\n",
+    "m.solve(solver_name=\"highs\", output_flag=False)\n",
     "sol = m.solution.to_dataframe()\n",
     "sol.plot(grid=True, ylabel=\"Optimal Value\")"
    ]
@@ -242,7 +242,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "m.solve(solver_name=\"highs\")\n",
+    "m.solve(solver_name=\"highs\", output_flag=False)\n",
     "sol = m.solution.to_dataframe()\n",
     "sol.plot(grid=True, ylabel=\"Optimal Value\")"
    ]
@@ -276,7 +276,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "m.solve(solver_name=\"highs\")\n",
+    "m.solve(solver_name=\"highs\", output_flag=False)\n",
     "sol = m.solution.to_dataframe()\n",
     "sol.plot(grid=True, ylabel=\"Optimal Value\")"
    ]
@@ -326,7 +326,7 @@
     "# Penalize activation of z in the objective\n",
     "m.objective = x + 3 * y + 10 * z\n",
     "\n",
-    "m.solve(solver_name=\"highs\")"
+    "m.solve(solver_name=\"highs\", output_flag=False)"
    ]
   },
   {
@@ -346,7 +346,7 @@
    "source": [
     "m.variables.binaries.fix()\n",
     "m.variables.binaries.relax()\n",
-    "m.solve(solver_name=\"highs\")\n",
+    "m.solve(solver_name=\"highs\", output_flag=False)\n",
     "\n",
     "# Dual values are now available on the constraints\n",
     "m.constraints[\"con1\"].dual"
diff --git a/examples/transport-tutorial.ipynb b/examples/transport-tutorial.ipynb
index b42e67e8..cd5cdccd 100644
--- a/examples/transport-tutorial.ipynb
+++ b/examples/transport-tutorial.ipynb
@@ -417,7 +417,7 @@
    "outputs": [],
    "source": [
     "# Solve the model\n",
-    "m.solve(solver_name=\"highs\")"
+    "m.solve(solver_name=\"highs\", output_flag=False)"
    ]
   },
   {

From 6d61112ec588a2b56e8c664a0bcebea9a8c53273 Mon Sep 17 00:00:00 2001
From: FBumann <117816358+FBumann@users.noreply.github.com>
Date: Mon, 11 May 2026 15:24:47 +0200
Subject: [PATCH 2/2] docs: silence HiGHS console output in piecewise tutorials
 too
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Extends the log-silencing scope to the two piecewise tutorials, which
together call m.solve() nine times.  Same transformation as the other
notebooks — output_flag=False as a HiGHS-specific kwarg forwarded via
**solver_options.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
---
 examples/piecewise-inequality-bounds.ipynb  | 40 ++++++++++-----------
 examples/piecewise-linear-constraints.ipynb | 16 ++++-----
 2 files changed, 28 insertions(+), 28 deletions(-)

diff --git a/examples/piecewise-inequality-bounds.ipynb b/examples/piecewise-inequality-bounds.ipynb
index a79c612d..101f28d5 100644
--- a/examples/piecewise-inequality-bounds.ipynb
+++ b/examples/piecewise-inequality-bounds.ipynb
@@ -4,7 +4,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Piecewise inequalities \u2014 per-tuple sign\n",
+    "# Piecewise inequalities — per-tuple sign\n",
     "\n",
     "`add_piecewise_formulation` accepts an optional third tuple element, `\"<=\"` or `\">=\"`, that marks one expression as **bounded** by the piecewise curve instead of pinned to it:\n",
     "\n",
@@ -15,17 +15,17 @@
     ")\n",
     "```\n",
     "\n",
-    "This notebook walks through the geometry, the curvature \u00d7 sign matching that lets `method=\"auto\"` skip MIP machinery entirely, and the feasible regions produced by each method (LP, SOS2, incremental). For the formulation math see the [reference page](piecewise-linear-constraints).\n",
+    "This notebook walks through the geometry, the curvature × sign matching that lets `method=\"auto\"` skip MIP machinery entirely, and the feasible regions produced by each method (LP, SOS2, incremental). For the formulation math see the [reference page](piecewise-linear-constraints).\n",
     "\n",
     "## Key points\n",
     "\n",
     "| Tuple form | Behaviour |\n",
     "|---|---|\n",
     "| `(expr, breaks)` | Pinned: `expr` lies exactly on the curve. |\n",
-    "| `(expr, breaks, \"<=\")` | Bounded above: `expr \u2264 f(other tuples)`. |\n",
-    "| `(expr, breaks, \">=\")` | Bounded below: `expr \u2265 f(other tuples)`. |\n",
+    "| `(expr, breaks, \"<=\")` | Bounded above: `expr ≤ f(other tuples)`. |\n",
+    "| `(expr, breaks, \">=\")` | Bounded below: `expr ≥ f(other tuples)`. |\n",
     "\n",
-    "Currently at most one tuple may carry a non-equality sign, and 3+ tuples must all be equality. Multi-bounded and N\u22653 inequality cases aren't supported yet \u2014 if you have a concrete use case, please open an issue at https://github.com/PyPSA/linopy/issues so we can scope it properly."
+    "Currently at most one tuple may carry a non-equality sign, and 3+ tuples must all be equality. Multi-bounded and N≥3 inequality cases aren't supported yet — if you have a concrete use case, please open an issue at https://github.com/PyPSA/linopy/issues so we can scope it properly."
    ]
   },
   {
@@ -48,7 +48,7 @@
   {
    "cell_type": "markdown",
    "metadata": {},
-   "source": "## Setup \u2014 a concave curve\n\nWe use a concave, monotonically increasing curve. With a tuple bounded `<=`, the LP method is applicable (concave + `<=` is a tight relaxation)."
+   "source": "## Setup — a concave curve\n\nWe use a concave, monotonically increasing curve. With a tuple bounded `<=`, the LP method is applicable (concave + `<=` is a tight relaxation)."
   },
   {
    "cell_type": "code",
@@ -79,11 +79,11 @@
     "\n",
     "With one tuple bounded `<=` and our concave curve, the three methods give the **same** feasible region within `[x_0, x_n]`:\n",
     "\n",
-    "- **`method=\"lp\"`** \u2014 tangent lines + domain bounds. No auxiliary variables.\n",
-    "- **`method=\"sos2\"`** \u2014 lambdas + SOS2 + split link (pinned equality, bounded signed). Solver picks the piece.\n",
-    "- **`method=\"incremental\"`** \u2014 delta fractions + binaries + split link. Same mathematics, MIP encoding instead of SOS2.\n",
+    "- **`method=\"lp\"`** — tangent lines + domain bounds. No auxiliary variables.\n",
+    "- **`method=\"sos2\"`** — lambdas + SOS2 + split link (pinned equality, bounded signed). Solver picks the piece.\n",
+    "- **`method=\"incremental\"`** — delta fractions + binaries + split link. Same mathematics, MIP encoding instead of SOS2.\n",
     "\n",
-    "`method=\"auto\"` dispatches to `\"lp\"` whenever applicable \u2014 it's always preferable because it's pure LP.\n",
+    "`method=\"auto\"` dispatches to `\"lp\"` whenever applicable — it's always preferable because it's pure LP.\n",
     "\n",
     "Let's verify they produce the same solution at `power=15`."
    ]
@@ -98,17 +98,17 @@
     }
    },
    "outputs": [],
-   "source": "def solve(method, power_val):\n    m = linopy.Model()\n    power = m.add_variables(lower=0, upper=30, name=\"power\")\n    fuel = m.add_variables(lower=0, upper=40, name=\"fuel\")\n    m.add_piecewise_formulation(\n        (fuel, y_pts, \"<=\"),  # bounded\n        (power, x_pts),  # pinned\n        method=method,\n    )\n    m.add_constraints(power == power_val)\n    m.add_objective(-fuel)  # maximise fuel to push against the bound\n    m.solve()\n    return float(m.solution[\"fuel\"]), list(m.variables), list(m.constraints)\n\n\nfor method in [\"lp\", \"sos2\", \"incremental\"]:\n    fuel_val, vars_, cons_ = solve(method, 15)\n    print(f\"{method:12}: fuel={fuel_val:.2f}  vars={vars_}  cons={cons_}\")"
+   "source": "def solve(method, power_val):\n    m = linopy.Model()\n    power = m.add_variables(lower=0, upper=30, name=\"power\")\n    fuel = m.add_variables(lower=0, upper=40, name=\"fuel\")\n    m.add_piecewise_formulation(\n        (fuel, y_pts, \"<=\"),  # bounded\n        (power, x_pts),  # pinned\n        method=method,\n    )\n    m.add_constraints(power == power_val)\n    m.add_objective(-fuel)  # maximise fuel to push against the bound\n    m.solve(output_flag=False)\n    return float(m.solution[\"fuel\"]), list(m.variables), list(m.constraints)\n\n\nfor method in [\"lp\", \"sos2\", \"incremental\"]:\n    fuel_val, vars_, cons_ = solve(method, 15)\n    print(f\"{method:12}: fuel={fuel_val:.2f}  vars={vars_}  cons={cons_}\")"
   },
   {
    "cell_type": "markdown",
    "metadata": {},
-   "source": "All three give `fuel=25` at `power=15` (which is `f(15)` exactly) \u2014 the math is equivalent. The LP method is strictly cheaper: no auxiliary variables, just three chord constraints and two domain bounds.\n\nThe SOS2 and incremental methods create lambdas (or deltas + binaries) and split the link into a pinned-equality constraint plus a signed bounded link \u2014 but the feasible region is the same."
+   "source": "All three give `fuel=25` at `power=15` (which is `f(15)` exactly) — the math is equivalent. The LP method is strictly cheaper: no auxiliary variables, just three chord constraints and two domain bounds.\n\nThe SOS2 and incremental methods create lambdas (or deltas + binaries) and split the link into a pinned-equality constraint plus a signed bounded link — but the feasible region is the same."
   },
   {
    "cell_type": "markdown",
    "metadata": {},
-   "source": "## Visualising the feasible region\n\nThe feasible region for `(power, fuel)` with `fuel` bounded `<=` is the **hypograph** of `f` restricted to the curve's x-domain:\n\n$$\\{ (x, y) : x_0 \\le x \\le x_n,\\ y \\le f(x) \\}$$\n\nWe colour green feasible points, red infeasible ones. Three test points:\n\n- `(15, 15)` \u2014 inside the curve, `15 \u2264 f(15)=25` \u2713\n- `(15, 25)` \u2014 on the curve \u2713\n- `(15, 29)` \u2014 above `f(15)`, should be infeasible \u2717\n- `(35, 20)` \u2014 power beyond domain, infeasible \u2717"
+   "source": "## Visualising the feasible region\n\nThe feasible region for `(power, fuel)` with `fuel` bounded `<=` is the **hypograph** of `f` restricted to the curve's x-domain:\n\n$$\\{ (x, y) : x_0 \\le x \\le x_n,\\ y \\le f(x) \\}$$\n\nWe colour green feasible points, red infeasible ones. Three test points:\n\n- `(15, 15)` — inside the curve, `15 ≤ f(15)=25` ✓\n- `(15, 25)` — on the curve ✓\n- `(15, 29)` — above `f(15)`, should be infeasible ✗\n- `(35, 20)` — power beyond domain, infeasible ✗"
   },
   {
    "cell_type": "code",
@@ -144,7 +144,7 @@
     "ax.set(\n",
     "    xlabel=\"power\",\n",
     "    ylabel=\"fuel\",\n",
-    "    title=\"sign='<=' feasible region \u2014 hypograph of f(x) on [x_0, x_n]\",\n",
+    "    title=\"sign='<=' feasible region — hypograph of f(x) on [x_0, x_n]\",\n",
     ")\n",
     "ax.grid(alpha=0.3)\n",
     "ax.legend()\n",
@@ -157,16 +157,16 @@
    "source": [
     "## When is LP the right choice?\n",
     "\n",
-    "`tangent_lines` imposes the **intersection** of chord inequalities. Whether that intersection matches the true hypograph/epigraph of `f` depends on the curvature \u00d7 sign combination:\n",
+    "`tangent_lines` imposes the **intersection** of chord inequalities. Whether that intersection matches the true hypograph/epigraph of `f` depends on the curvature × sign combination:\n",
     "\n",
     "| curvature | bounded `<=` | bounded `>=` |\n",
     "|-----------|--------------|--------------|\n",
-    "| **concave** | **hypograph (exact \u2713)** | **wrong region** \u2014 requires `y \u2265 max_k chord_k(x) > f(x)` |\n",
-    "| **convex**  | **wrong region** \u2014 requires `y \u2264 min_k chord_k(x) < f(x)` | **epigraph (exact \u2713)** |\n",
+    "| **concave** | **hypograph (exact ✓)** | **wrong region** — requires `y ≥ max_k chord_k(x) > f(x)` |\n",
+    "| **convex**  | **wrong region** — requires `y ≤ min_k chord_k(x) < f(x)` | **epigraph (exact ✓)** |\n",
     "| linear      | exact | exact |\n",
     "| mixed (non-convex) | convex hull of `f` (wrong for exact hypograph) | concave hull of `f` (wrong for exact epigraph) |\n",
     "\n",
-    "In the \u2717 cases, tangent lines do **not** give a loose relaxation \u2014 they give a **strictly wrong feasible region** that rejects points satisfying the true constraint. Example: for a concave `f` with `y \u2265 f(x)`, the chord of any piece extrapolated over another piece's x-range lies *above* `f`, so `y \u2265 max_k chord_k(x)` forbids `y = f(x)` itself.\n",
+    "In the ✗ cases, tangent lines do **not** give a loose relaxation — they give a **strictly wrong feasible region** that rejects points satisfying the true constraint. Example: for a concave `f` with `y ≥ f(x)`, the chord of any piece extrapolated over another piece's x-range lies *above* `f`, so `y ≥ max_k chord_k(x)` forbids `y = f(x)` itself.\n",
     "\n",
     "`method=\"auto\"` dispatches to LP only in the two **exact** cases (concave + `<=` or convex + `>=`). For the other combinations it falls back to SOS2 or incremental, which encode the hypograph/epigraph exactly via discrete piece selection.\n",
     "\n",
@@ -185,12 +185,12 @@
     }
    },
    "outputs": [],
-   "source": "# 1. Non-convex curve: auto falls back (LP relaxation would be loose)\nx_nc = [0, 10, 20, 30]\ny_nc = [0, 20, 10, 30]  # slopes change sign \u2192 mixed convexity\n\nm1 = linopy.Model()\nx1 = m1.add_variables(lower=0, upper=30, name=\"x\")\ny1 = m1.add_variables(lower=0, upper=40, name=\"y\")\nf1 = m1.add_piecewise_formulation((y1, y_nc, \"<=\"), (x1, x_nc))\nprint(f\"non-convex + '<=' \u2192 {f1.method}\")\n\n# 2. Concave curve + sign='>=': LP would be loose \u2192 auto falls back to MIP\nx_cc = [0, 10, 20, 30]\ny_cc = [0, 20, 30, 35]  # concave\n\nm2 = linopy.Model()\nx2 = m2.add_variables(lower=0, upper=30, name=\"x\")\ny2 = m2.add_variables(lower=0, upper=40, name=\"y\")\nf2 = m2.add_piecewise_formulation((y2, y_cc, \">=\"), (x2, x_cc))\nprint(f\"concave + '>='    \u2192 {f2.method}\")\n\n# 3. Explicit method=\"lp\" with mismatched curvature raises\ntry:\n    m3 = linopy.Model()\n    x3 = m3.add_variables(lower=0, upper=30, name=\"x\")\n    y3 = m3.add_variables(lower=0, upper=40, name=\"y\")\n    m3.add_piecewise_formulation((y3, y_cc, \">=\"), (x3, x_cc), method=\"lp\")\nexcept ValueError as e:\n    print(f\"lp(concave, '>=')  \u2192 raises: {e}\")"
+   "source": "# 1. Non-convex curve: auto falls back (LP relaxation would be loose)\nx_nc = [0, 10, 20, 30]\ny_nc = [0, 20, 10, 30]  # slopes change sign → mixed convexity\n\nm1 = linopy.Model()\nx1 = m1.add_variables(lower=0, upper=30, name=\"x\")\ny1 = m1.add_variables(lower=0, upper=40, name=\"y\")\nf1 = m1.add_piecewise_formulation((y1, y_nc, \"<=\"), (x1, x_nc))\nprint(f\"non-convex + '<=' → {f1.method}\")\n\n# 2. Concave curve + sign='>=': LP would be loose → auto falls back to MIP\nx_cc = [0, 10, 20, 30]\ny_cc = [0, 20, 30, 35]  # concave\n\nm2 = linopy.Model()\nx2 = m2.add_variables(lower=0, upper=30, name=\"x\")\ny2 = m2.add_variables(lower=0, upper=40, name=\"y\")\nf2 = m2.add_piecewise_formulation((y2, y_cc, \">=\"), (x2, x_cc))\nprint(f\"concave + '>='    → {f2.method}\")\n\n# 3. Explicit method=\"lp\" with mismatched curvature raises\ntry:\n    m3 = linopy.Model()\n    x3 = m3.add_variables(lower=0, upper=30, name=\"x\")\n    y3 = m3.add_variables(lower=0, upper=40, name=\"y\")\n    m3.add_piecewise_formulation((y3, y_cc, \">=\"), (x3, x_cc), method=\"lp\")\nexcept ValueError as e:\n    print(f\"lp(concave, '>=')  → raises: {e}\")"
   },
   {
    "cell_type": "markdown",
    "metadata": {},
-   "source": "## Summary\n\n- Default is all-equality: every tuple lies on the curve.\n- Append `\"<=\"` or `\">=\"` as a third tuple element to mark one expression as bounded by the curve.\n- `method=\"auto\"` picks the most efficient formulation: LP for matching-curvature 2-variable inequalities, otherwise SOS2 or incremental.\n- At most one tuple may be bounded; with 3+ tuples all must be equality. Multi-bounded and N\u22653 inequality use cases \u2014 please open an issue at https://github.com/PyPSA/linopy/issues so we can scope them."
+   "source": "## Summary\n\n- Default is all-equality: every tuple lies on the curve.\n- Append `\"<=\"` or `\">=\"` as a third tuple element to mark one expression as bounded by the curve.\n- `method=\"auto\"` picks the most efficient formulation: LP for matching-curvature 2-variable inequalities, otherwise SOS2 or incremental.\n- At most one tuple may be bounded; with 3+ tuples all must be equality. Multi-bounded and N≥3 inequality use cases — please open an issue at https://github.com/PyPSA/linopy/issues so we can scope them."
   }
  ],
  "metadata": {
diff --git a/examples/piecewise-linear-constraints.ipynb b/examples/piecewise-linear-constraints.ipynb
index 392ca8f1..fe1da9b8 100644
--- a/examples/piecewise-linear-constraints.ipynb
+++ b/examples/piecewise-linear-constraints.ipynb
@@ -81,7 +81,7 @@
     "pwf = m.add_piecewise_formulation((power, x_pts), (fuel, y_pts))\n",
     "m.add_constraints(power == demand, name=\"demand\")\n",
     "m.add_objective(fuel.sum())\n",
-    "m.solve(reformulate_sos=\"auto\")\n",
+    "m.solve(reformulate_sos=\"auto\", output_flag=False)\n",
     "\n",
     "print(pwf)  # inspect the auto-resolved method\n",
     "m.solution[[\"power\", \"fuel\"]].to_pandas()"
@@ -136,7 +136,7 @@
     "    m.add_piecewise_formulation((power, x_pts), (fuel, y_pts), method=method)\n",
     "    m.add_constraints(power == demand, name=\"demand\")\n",
     "    m.add_objective(fuel.sum())\n",
-    "    m.solve(reformulate_sos=\"auto\")\n",
+    "    m.solve(reformulate_sos=\"auto\", output_flag=False)\n",
     "    return m.solution[\"fuel\"].to_pandas()\n",
     "\n",
     "\n",
@@ -175,7 +175,7 @@
     ")\n",
     "m.add_constraints(power + backup == xr.DataArray([15, 60, 75], coords=[time]))\n",
     "m.add_objective(cost.sum() + 10 * backup.sum())\n",
-    "m.solve(reformulate_sos=\"auto\")\n",
+    "m.solve(reformulate_sos=\"auto\", output_flag=False)\n",
     "m.solution[[\"power\", \"cost\", \"backup\"]].to_pandas()"
    ]
   },
@@ -225,7 +225,7 @@
     ")\n",
     "m.add_constraints(power == xr.DataArray([30, 80, 100], coords=[time]))\n",
     "m.add_objective(-fuel.sum())  # push fuel against the bound\n",
-    "m.solve(reformulate_sos=\"auto\")\n",
+    "m.solve(reformulate_sos=\"auto\", output_flag=False)\n",
     "\n",
     "print(f\"resolved method={pwf.method}, curvature={pwf.convexity}\")\n",
     "m.solution[[\"power\", \"fuel\"]].to_pandas()"
@@ -282,7 +282,7 @@
     "# demand below p_min at t=1 — commit must be 0 and backup covers it\n",
     "m.add_constraints(power + backup == xr.DataArray([15, 80, 40], coords=[time]))\n",
     "m.add_objective(fuel.sum() + 50 * commit.sum() + 200 * backup.sum())\n",
-    "m.solve(reformulate_sos=\"auto\")\n",
+    "m.solve(reformulate_sos=\"auto\", output_flag=False)\n",
     "m.solution[[\"commit\", \"power\", \"fuel\", \"backup\"]].to_pandas()"
    ]
   },
@@ -330,7 +330,7 @@
     ")\n",
     "m.add_constraints(fuel == xr.DataArray([20, 100, 160], coords=[time]))\n",
     "m.add_objective(power.sum())\n",
-    "m.solve(reformulate_sos=\"auto\")\n",
+    "m.solve(reformulate_sos=\"auto\", output_flag=False)\n",
     "m.solution[[\"power\", \"fuel\", \"heat\"]].to_pandas().round(2)"
    ]
   },
@@ -388,7 +388,7 @@
     "m.add_piecewise_formulation((power, x_gen), (fuel, y_gen))\n",
     "m.add_constraints(power.sum(\"gen\") == xr.DataArray([80, 120, 50], coords=[time]))\n",
     "m.add_objective(fuel.sum())\n",
-    "m.solve(reformulate_sos=\"auto\")\n",
+    "m.solve(reformulate_sos=\"auto\", output_flag=False)\n",
     "m.solution[[\"power\", \"fuel\"]].to_dataframe()"
    ]
   },
@@ -417,7 +417,7 @@
     ")\n",
     "m.add_constraints(power == demand, name=\"demand\")\n",
     "m.add_objective(fuel.sum())\n",
-    "m.solve(reformulate_sos=\"auto\")\n",
+    "m.solve(reformulate_sos=\"auto\", output_flag=False)\n",
     "\n",
     "m.solution[[\"power\", \"fuel\"]].to_pandas()"
    ]