Optimization of Positive Generalized Polynomials under $ \boldsymbol{l^p}$ Constraints     constrained optimization  convex optimization  combinatorial optimization  subhomogeneous functions  labeling       font style='font-size:12px;'> 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...

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Non-Coercive Variational Problems with Constraints on the Derivatives      Non-Coercive Variational Problems  Derivatives  Constraints       font style='font-size:12px;'> 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)=...

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Relationship Between Dynamic Programming and the Maximum Principle under State Constraints     Dynamic Programming  Maximum Principle  State Constraints       font style='font-size:12px;'> 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...

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Variational Problems with Pointwise Constraints on the Derivatives      Variational problems  Topological methods  Pointwise constraints on the laplacian  Nonsmooth analysis  Subgradients       font style='font-size:12px;'> 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...

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Existence of a Continuous Solution of Parametric Nonlinear Equation with Constraints     Continuous Solution  Parametric Nonlinear Equation  Constraints       font style='font-size:12px;'> 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...

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