Shape evolutions under state constraints: A viability theorem

Semiparametric Estimation under Shape Constraints

Substantial structure and restrictions, such as monotonicity and curvature constraints, necessary to give economic interpretation to empirical findings are often furnished by economic theories. Although such restrictions may be imposed in certain parametric empirical settings in a relatively straightforward fashion, incorporating such restrictions in semiparametric models is often problematic. ...

Optimal Control under State Constraints

Optimal control under state constraints has brought new mathematical challenges that have led to new techniques and new theories. We survey some recent results related to issues of regularity of optimal trajectories, optimal controls and the value function, and discuss optimal synthesis and necessary optimality conditions. We also show how abstract inverse mapping theorems of set-valued analysi...

Semiparametric Binary Regression Models under Shape Constraints

We consider estimation of the regression function in a semiparametric binary regression model defined through an appropriate link function (with emphasis on the logistic link) using likelihood-ratio based inversion. The dichotomous response variable ∆ is influenced by a set of covariates that can be partitioned as (X,Z) where Z (real valued) is the covariate of primary interest and X (vector va...

Optimal Shape Coding under Buffer Constraints

In this paper, we consider an optimal rate control algorithm for shape coding of emerging MPEG-4 compression system. Current MPEG-4 shape coding consists of two sub-steps; First distortion is introduced by scaling down and up way. Then, second, context-based arithmetic coding is applied. Since the arithmetic coding is \lossless", scaling down and up step is considered as a virtual quantizer. We...

Viability Solutions to Structured Hamilton-Jacobi Equations under Constraints