Subgradients. A function f : Q ✓ R ! R defined on a convex domain Q is said to be convex if every point x 2 Q has a non-empty subgradient @f(x) = {g 2 R; f(y) f(x) + g>(y x), 8y 2 Q}. Geometrically, this means that a function is convex iff it is the maximum of all its supporting hyperplanes, i.e. f(x) = max x0,g2@f(x0) f(x0) + g > (x x0). When there is a unique element in @f(x) we call it the g...

Stochastic search involves finding a set of controllable parameters that minimizes an unknown objective function using a set of noisy observations. We consider the case when the unknown function is convex and a metamodel is used as a surrogate objective function. Often the data are non-i.i.d. and include a observable state variable, such as applicant information in a loan rate decision problem....

Abstract We propose a new decomposition method to solve multistage non-convex mixed-integer (stochastic) nonlinear programming problems (MINLPs). call this algorithm nested Benders (NC-NBD). NC-NBD is based on solving dynamically improved linear outer approximations of the MINLP, obtained by piecewise relaxations functions. Those MILPs are solved global optimality using an enhancement decomposi...

Abstract The problem of estimating the Domain of Attraction (DA) of equilibria of polynomial systems is considered. Specifically, the computation of the quadratic Lyapunov function which maximizes the volume of the estimate is addressed. In order to solve this double non-convex optimization problem, a semi-convex approach based on Linear Matrix Inequalities (LMIs) is proposed. Moreover, for the...

Mobile cloud computing (MCC) is a new technology that has been developed to overcome the restrictions of smart mobile devices (e.g. battery, processing power, storage capacity, etc.) to send a part of the program (with complex computing) to the cloud server (CS). In this paper, we study a multi-cell with multi-input and multi-output (MIMO) system in which the cell-interior users request service...