Vintage capital growth models have been at the heart of growth theory in the 60s. This research line collapsed in the late 60s with the so-called embodiment controversy and the technical sophisitication of the vintage models. This paper analyzes the astonishing revival of this literature in the 90s. In particular, it outlines three methodological breakthroughs explaining this resurgence: a grow...

Control parameterization technique is an effective method to solve optimal control problems. It works by approximating the function piece-wise constant (or linear) function. In this way, problems are approximated parameter selection problems, which can be regarded as finite-dimensional optimization where heights and switching times of taken decision variables. They solved using gradient-based m...

The optimal control problem for time-invariant linear systems with quadratic cost is considered for arbitrary, i.e., non-necessarily positive semidefinite, terminal cost matrices. A classification of such matrices is proposed, based on the maximum horizon for which there is a finite minimum cost for all initial states. When such an horizon is infinite, the classification is further refined, bas...

We construct a time-consistent sublinear expectation in the setting of volatility uncertainty. This mapping extends Peng's G-expectation by allowing the range of the volatility uncertainty to be stochastic. Our construction is purely probabilistic and based on an optimal control formulation with path-dependent control sets.

We consider the problem of boundary stabilization for a quasilinear 2×2 system of first-order hyperbolic PDEs. We design a full-state feedback control law, with actuation on only one end of the domain, and prove local H exponential stability of the closed-loop system. The proof of stability is based on the construction of a strict Lyapunov function. The feedback law is found using the recently ...

This paper explains how to stabilize a “nonholonomic integrator” using a hybrid control law employing switching and logic. Results concerning asymptotic stability and exponential convergence to the origin are derived. The notion of a (positively) invariant set is extended to hybrid systems and sufficient conditions for invariance are presented. The verification of these conditions does not requ...

Bidding for multi-items in simultaneous auctions raises challenging problems. In multi-auction settings, the determination of optimal bids by potential buyers requires combinatorial calculations. While an optimal bidding strategy is known when bidding in sequential auctions, only suboptimal strategies are available when bidding for items being sold in simultaneous auctions. We investigate a mul...

background: determining the optimal and effective scheme for administrating the chemotherapy agents in breast cancer is the main goal of this scientific research. the most important issue here is the amount of drug or radiation administrated in chemotherapy and radiotherapy for increasing patient's survival. this is because in these cases, the therapy not only kills the tumor cells, but also ki...