On solution uniqueness for Dezin problem analog for model parabolic hyperbolic type equation

In this paper investigated a problem with Dezin type condition for parabolic-hyperbolic mixed type equation. It is established a criterion for solution uniqueness to the problem.

Fractional Diffusion–Wave Equation with Application in Electrodynamics

We consider a diffusion–wave equation with fractional derivative with respect to the time variable, defined on infinite interval, and with the starting point at minus infinity. For this equation, we solve an asympotic boundary value problem without initial conditions, construct a representation of its solution, find out sufficient conditions providing solvability and solution uniqueness, and give some applications in fractional electrodynamics.

Fuzzy weak link approach to the two stage DEA

This paper refers to a recent approach to two-stage DEA called the weak link approach. It underlines the lack of solution uniqueness in this approach to DEA and the fact that in order for the solution to the weak link approach to be unique, the decision maker needs to express a preference on which Pareto solution would be most satisfactory. In this paper, we propose to use a fuzzy set approach called fuzzy bicriterial programming to help the decision maker to express this preference. Fuzzy bicriterial programming is explained and then applied to the weak link approach to the DEA. It is shown that for each candidate (Pareto) solution to the original weak link approach, there exists an expert opinion that can lead to the unequivocal selection of this solution due to the use of the fuzzy approach. The proposal is illustrated with examples.

Solution uniqueness of convex piecewise affine functions based optimization with applications to constrained ℓ1 minimization

In this paper, we study the solution uniqueness of an individual feasible vector of a class of convex optimization problems involving convex piecewise affine functions and subject to general polyhedral constraints. This class of problems incorporates many important polyhedral constrained ℓ1 recovery problems arising from sparse optimization, such as basis pursuit, LASSO, and basis pursuit denoising, as well as polyhedral gauge recovery. By leveraging the max-formulation of convex piecewise affine functions and convex analysis tools, we develop dual variables based necessary and sufficient uniqueness conditions via simple and yet unifying approaches; these conditions are applied to a wide range of ℓ1 minimization problems under possible polyhedral constraints. An effective linear program based scheme is proposed to verify solution uniqueness conditions. The results obtained in this paper not only recover the known solution uniqueness conditions in the literature by removing restrictive assumptions but also yield new uniqueness conditions for much broader constrained ℓ1-minimization problems.