5 papers
Optimizing Static Linear Feedback: Gradient Method
Ilyas Fatkhullin, Boris Polyak
The linear quadratic regulator is the fundamental problem of optimal control. Its state feedback version was set and solved in the early 1960s. However the static output feedback p…
Sparse solutions of optimal control via Newton method for under-determined systems
Boris Polyak, Andrey Tremba
We focus on finding sparse and least--norm solutions for unconstrained nonlinear optimal control problems. Such optimization problems are non-convex and non-smooth, neverth…
Gradient projection and conditional gradient methods for constrained nonconvex minimization
Maxim Balashov, Boris Polyak, Andrey Tremba
Minimization of a smooth function on a sphere or, more generally, on a smooth manifold, is the simplest non-convex optimization problem. It has a lot of applications. Our goal is t…
Non-monotone Behavior of the Heavy Ball Method
Marina Danilova, Anastasiya Kulakova, Boris Polyak
We focus on the solutions of second-order stable linear difference equations and demonstrate that their behavior can be non-monotone and exhibit peak effects depending on initial c…
Geometry of quadratic maps via convex relaxation
Anatoly Dymarsky, Elena Gryazina, Sergei Volodin +1
We consider several basic questions pertaining to the geometry of image of a general quadratic map. In general the image of a quadratic map is non-convex, although there are severa…