In this paper a condition number for linear-quadratic two-stage stochastic optimization problems is introduced as the Lipschitz modulus of the multifunction assigning to a (discrete) probability distribution the solution set of the problem. Being the outer norm of the Mordukhovich coderivative of this multifunction, the condition number canbe estimated fromabove explicitly in termsof the proble...

We show that delaying fully-expansive proof reconstruction for non-interactive decision procedures can result in a more efficient workflow. In contrast with earlier work, our approach to postponed proof does not require making deep changes to the theorem prover.

In this paper, the concept of completely N-continuous multifunction is defined and their basic characterizations and properties are obtained.

The purpose of this paper is to introduce a modified Halpern-type iteration algorithm and prove strong convergence of the algorithm for quasi-φ-asymptotically non-expansive mappings. Our results improve and extend the corresponding results announced by many others.

We propose a projection-type algorithm for variational inequalities involving multifunction. The algorithm requires two projections on the constraint set only in a part of iterations (one third of the subcases). For the other iterations, only one projection is used. A global convergence is proved under the weak assumption that the multifunction of the problem is pseudomonotone at a solution, cl...

Engineering problems shunned previously rise to the surface gradually with the activities of reforming the natural world in depth, the problem of expansive soil crack under the changing environment becoming a control factor of expansive soil slope stability. The problem of expansive soil crack has gradually become a research hotspot, elaborates the occurrence and development of cracks from the ...

Expansive soils swell when they absorb water and shrink when water evaporates from them. Hence, lightly loaded civil engineering structures founded in these soils are subjected to severe distress. Therefore, there is a need to ameliorate or improve these swelling soils through some innovative methods. This paper discusses chemical stabilisation of expansive soils, a technique in which chemical ...

Under mild assumptions, we prove that any random multifunction can be represented as the set of minimizers an infinitely many differentiable normal integrand, which preserves convexity multifunction. This result is extended version work done by Azagra and Ferrera (Proc Am Math Soc 130(12):3687–3692, 2002). We provide several applications this to approximation multifunctions integrands. The pape...