We provide Completely Positive and Copositive Optimization formulations for the Constrained Fractional Quadratic Problem (CFQP) and Standard Fractional Quadratic Problem (StFQP). Based on these formulations, Semidefinite Programming (SDP) relaxations are derived for finding good lower bounds to these fractional programs, which can be used in a global optimization branch-and-bound approach. Appl...

We describe the solution of a bound constrained convex quadratic problem with limited memory resources. The problem arises from physical simulations occurring within video games. The motivating problem is outlined, along with a simple interior point approach for its solution. Various linear algebra issues arising in the implementation are explored, including preconditioning, ordering and a numb...

This report covers the application of a piecewise-linear approximation to a quadratic program, QP. In this case the program is one that solves 3D conformal radiation treatment problem and returns optimal beam weights. Four different methods of approximating the quadratic problem were tested and compared to each other and the original problem. The methods are δ method, λ method, σ method, and γ ...

3 Quadratic Optimal Control 5 3.1 Linear Quadratic Optimal State Regulator Design . . . . . . . . . . . . . . . . . 6 3.2 Linear Quadratic Optimal Output Regulator Design . . . . . . . . . . . . . . . . 9 3.3 Stability of LQ controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.4 Linear Quadratic Gaussian (LQG) Control . . . . . . . . . . . . . . . . . . . . . 11 3.4.1 S...

We consider a simple class of stochastic control problems with delayed control, in both the drift and diffusion part state differential equation. provide new characterization solution terms set Riccati partial equations. Existence uniqueness are obtained under sufficient condition expressed directly as relation between time horizon, drift, volatility delay. Furthermore, deep learning scheme (Th...