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Constraints on hypothetical counterexamples to the Casas-Alvero conjecture
Casas-Alvero conjecture polynomials Complex Variables
2012/4/18
The Casas-Alvero conjecture states: if a complex univariate polynomial has a common root with each of its derivatives, then it has a unique root. We show that hypothetical counterexamples must have at...
Optimization of Positive Generalized Polynomials under $ \boldsymbol{l^p}$ Constraints
constrained optimization convex optimization combinatorial optimization subhomogeneous functions labeling
2009/1/23
The problem of maximizing a non-negative generalized polynomial of degree at most $p$ on the $l_p$-sphere is shown to be equivalent to a concave one. Arguments where the maximum is attained are charac...
Non-Coercive Variational Problems with Constraints on the Derivatives
Non-Coercive Variational Problems Derivatives Constraints
2009/1/22
We establish a necessary and sufficient condition for the existence of the minimum of the functional $\dis{\int_0^1} f(t,v^\prime(t))dt$ in the class ${\cal W}_d^p=\{v\in W^{1,p}([0,1]): v(0)=0, v(1)=...
Relationship Between Dynamic Programming and the Maximum Principle under State Constraints
Dynamic Programming Maximum Principle State Constraints
2009/1/22
Bellman's dynamic programming and Pontryagin's maximum principle are two basic tools for studying optimal control theory. We consider the optimal control problem under state constraints and examine th...
Variational Problems with Pointwise Constraints on the Derivatives
Variational problems Topological methods Pointwise constraints on the laplacian Nonsmooth analysis Subgradients
2009/1/22
This paper is concerned with the solvability of a class of nonlinear variational inequalities involving pointwise unilateral constraints on the laplacian. We describe the set of the pairs $(\psi,h)$ o...
Existence of a Continuous Solution of Parametric Nonlinear Equation with Constraints
Continuous Solution Parametric Nonlinear Equation Constraints
2009/1/16
Combining a consequence of the Michael continuous selection theorem and an iterative scheme we prove the existence of a continuous solution of a parametric equation with constraints. An inverse functi...