diff --git a/ignite/handlers/param_scheduler.py b/ignite/handlers/param_scheduler.py
index 7a878ce4fd1..d0d0cba4fd8 100644
--- a/ignite/handlers/param_scheduler.py
+++ b/ignite/handlers/param_scheduler.py
@@ -390,6 +390,9 @@ class LinearCyclicalScheduler(CyclicalScheduler):
         save_history: whether to log the parameter values to
             `engine.state.param_history`, (default=False).
         param_group_index: optimizer's parameters group to use.
+        monotonic: whether to schedule only one half of the cycle: descending or ascending.
+            If True, this argument can not be used together with ``warmup_duration``.
+            (default=False).
 
     Note:
         If the scheduler is bound to an 'ITERATION_*' event, 'cycle_size' should
@@ -465,12 +468,28 @@ def print_lr():
 
     .. versionchanged:: 0.4.13
         Added cyclic warm-up to the scheduler using ``warmup_duration``.
+
+    .. versionchanged:: 0.5.0
+        Added monotonic argument.
     """
 
+    def __init__(self, *args: Any, monotonic: bool = False, **kwagrs: Any):
+        super(LinearCyclicalScheduler, self).__init__(*args, **kwagrs)
+        self.monotonic = monotonic
+        if self.warmup_duration > 0 and not self.monotonic:
+            raise ValueError(
+                "Invalid combination when warmup_duration > 0 and monotonic=False, "
+                "please use either set warmup_duration=0 or monotonic=True"
+            )
+
     def get_param(self) -> float:
         """Method to get current optimizer's parameter value"""
         cycle_progress = self.event_index / self.cycle_size
-        return self.end_value + (self.start_value - self.end_value) * abs(cycle_progress - 0.5) * 2
+
+        if self.monotonic:
+            return self.start_value + (self.end_value - self.start_value) * cycle_progress
+        else:
+            return self.end_value + (self.start_value - self.end_value) * abs(cycle_progress - 0.5) * 2
 
 
 class CosineAnnealingScheduler(CyclicalScheduler):
diff --git a/tests/ignite/handlers/test_param_scheduler.py b/tests/ignite/handlers/test_param_scheduler.py
index eb70ab3a082..af5f5cae497 100644
--- a/tests/ignite/handlers/test_param_scheduler.py
+++ b/tests/ignite/handlers/test_param_scheduler.py
@@ -68,6 +68,13 @@ def test_linear_scheduler_asserts():
     with pytest.raises(ValueError, match=r"Argument cycle_size should be positive and larger than 1"):
         LinearCyclicalScheduler(optimizer, "lr", 1, 0, cycle_size=1)
 
+    with pytest.raises(
+        ValueError,
+        match=r"Invalid combination when warmup_duration > 0 and monotonic=False, "
+        r"please use either set warmup_duration=0 or monotonic=True",
+    ):
+        LinearCyclicalScheduler(optimizer, "lr", 1, 0, cycle_size=2, warmup_duration=1)
+
 
 def test_linear_scheduler():
     tensor = torch.zeros([1], requires_grad=True)
@@ -144,6 +151,102 @@ def save_lr(engine):
         scheduler.load_state_dict(state_dict)
 
 
+def test_linear_scheduler_warmup_duration():
+    tensor = torch.zeros([1], requires_grad=True)
+    optimizer = torch.optim.SGD([tensor], lr=0.0)
+
+    scheduler = LinearCyclicalScheduler(optimizer, "lr", 1, 0, 10, warmup_duration=5, monotonic=True)
+    state_dict = scheduler.state_dict()
+
+    def save_lr(engine):
+        lrs.append(optimizer.param_groups[0]["lr"])
+
+    trainer = Engine(lambda engine, batch: None)
+    trainer.add_event_handler(Events.ITERATION_STARTED, scheduler)
+    trainer.add_event_handler(Events.ITERATION_COMPLETED, save_lr)
+    lr_values_in_cycle = [
+        1.0,
+        0.9,
+        0.8,
+        0.7,
+        0.6,
+        0.5,
+        0.4,
+        0.3,
+        0.2,
+        0.1,
+        0.0,
+        0.2,
+        0.4,
+        0.6,
+        0.8,
+        1.0,
+        0.9,
+        0.8,
+        0.7,
+        0.6,
+    ]
+    for _ in range(2):
+        lrs = []
+        trainer.run([0] * 10, max_epochs=2)
+
+        assert lrs == pytest.approx(lr_values_in_cycle)
+        scheduler.load_state_dict(state_dict)
+
+    optimizer = torch.optim.SGD([tensor], lr=0)
+    scheduler = LinearCyclicalScheduler(optimizer, "lr", 1, 0, 10, cycle_mult=2, warmup_duration=5, monotonic=True)
+    state_dict = scheduler.state_dict()
+
+    trainer = Engine(lambda engine, batch: None)
+    trainer.add_event_handler(Events.ITERATION_STARTED, scheduler)
+    trainer.add_event_handler(Events.ITERATION_COMPLETED, save_lr)
+
+    for _ in range(2):
+        lrs = []
+        trainer.run([0] * 10, max_epochs=3)
+
+        assert lrs == list(
+            map(
+                pytest.approx,
+                [
+                    # Cycle 1
+                    1.0,
+                    0.9,
+                    0.8,
+                    0.7,
+                    0.6,
+                    0.5,
+                    0.4,
+                    0.3,
+                    0.2,
+                    0.1,
+                    0.0,
+                    0.2,
+                    0.4,
+                    0.6,
+                    0.8,
+                    # Cycle 2
+                    1.0,
+                    0.95,
+                    0.9,
+                    0.85,
+                    0.8,
+                    0.75,
+                    0.7,
+                    0.65,
+                    0.6,
+                    0.55,
+                    0.5,
+                    0.45,
+                    0.4,
+                    0.35,
+                    0.3,
+                ],
+            )
+        )
+        scheduler.load_state_dict(state_dict)
+
+
 def test_linear_scheduler_cycle_size_two():
     tensor = torch.zeros([1], requires_grad=True)
     optimizer = torch.optim.SGD([tensor], lr=0)