State-of-the-art methods in convex and non-convex optimization employ higher-order derivative information, either implicitly or explicitly. We explore the limitations of higher-order optimization and prove that even for convex optimization, a polynomial dependence on the approximation guarantee and higher-order smoothness parameters is necessary. As a special case, we show Nesterov’s accelerate...

INTRODUCTION Lymphedema is a relatively common phenomenon. It is important that clinicians appreciate the relative risks imposed by this condition. While for some it may only represent a flaw in appearance, this condition can potentially have fatal consequences. Our case reports on the challenges of cellulitis in a lymphedematous extremity that progressed to septic shock. CASE PRESENTATION A ...