Search

We found a minor error in the proof of paper “Universal Alignment Probability Revisited” by S.Y. Lin and Y.C. Ho (J. Optim. Theory Appl. 113(2):399–407, ). In this note, we give a counterexample and explain the reason. We also show that the conclusion of that paper is still correct despite this minor error. A new proof of the conclusion is given. [ABSTRACT FROM AUTHOR]

In this paper we study some optimization problems for nonlinear elastic membranes. More precisely, we consider the problem of optimizing the cost functional $\mathcal {J}(u)=\int_{\partial\Omega}f(x)u\,\mathrm {d}\mathcal {H}^{N-1}$ over some admissible class of loads f where u is the (unique) solution to the problem −Δ p u+| u| p−2 u=0 in Ω with | ∇ u| p−2 u ν= f on ∂Ω. [ABSTRACT FROM AUTHOR]

The notion of extended-well-posedness has been introduced by Zolezzi for scalar minimization problems and has been further generalized to vector minimization problems by Huang. In this paper, we study the extended well-posedness properties of vector minimization problems in which the objective function is C-quasiconvex. To achieve this task, we first study some stability properties of such problems. [ABSTRACT FROM AUTHOR]

In this paper, we give an analysis and a general procedure for 4D variational data assimilation (4D-Var). In functional partial differential equation setting, the adjoint equation method, sensitivity analysis, and multicomponent operator splitting are discussed. Nonlinear optimization methods and convergence analysis are also investigated for 4D-Var. [ABSTRACT FROM AUTHOR]

This paper develops two necessary conditions for a local minimum of an arbitrary extended real-valued function (Theorem 2.2) and, quite separately, two conditions, each sufficient for such a function to have a strict local minimum (Theorem 2.3). [ABSTRACT FROM AUTHOR]

In this paper, a class of global optimization problems is considered. Corresponding to each local minimizer obtained, we introduced a new modified function and construct a corresponding optimization subproblem with one constraint. Then, by applying a local search method to the one-constraint optimization subproblem and using the local minimizer as the starting point, we obtain a better local optimal solution. This process is continued iteratively. A termination rule is obtained which can serve as stopping criterion for the iterating process. To demonstrate the efficiency of the proposed approach, numerical examples are solved. [ABSTRACT FROM AUTHOR]