The paper presents complete characterizations of Lipschitzian full stability of locally optimal solutions to problems of second-order cone programming (SOCP) expressed entirely in terms of their initial data. These characterizations are obtained via appropriate versions of the quadratic growth and strong second-order sufficient conditions under the corresponding constraint qualifications. We al...

We derived the Kuhn-Tucker theorem by assuming regularity of the binding constraints. With the possibility of corner solutions, regularity is too stringent. The regularity condition will not necessarily apply throughout the constraint set. Verifying the regularity condition requires knowing the optimal solution, but the first-order conditions will not identify the optimal solution unless the re...

In this paper, we answer the question under which conditions the porousmedium equation with convection and with periodic boundary conditions possesses gradient-type Lyapunov functionals (first-order entropies). It is shown that the weighted sum of first-order and zeroth-order entropies are Lyapunov functionals if the weight for the zeroth-order entropy is sufficiently large, depending on the st...

Previous work has studied the classical joint economic lot size model as an adverse selection problem with asymmetric cost information. Solving this problem is challenging due to the presence of countervailing incentives and two-dimensional information asymmetry, under which the classical single-crossing condition does not need to hold. In the present work we advance the existing knowledge abou...

The determination of the appropriate boundary conditions for a two-dimensional theory of elastic flat plates (and shells) consistent with the expected order of accuracy of the theory is both critical and challenging. The reciprocal theorem of elasticity will be applied in a novel way to obtain the appropriate stress boundary conditions for plate bending accurate to all order (with respect to th...

The correlated demand caused by cross-selling, Zhang et al (2011) proposed a two-item EOQ model, where the unmet demand for the major item can be partially backordered with lost sales that will reduce demand for the minor item. They developed an enumeration algorithm that can deal with only one minor associated item. Zhang et al (2011) proposed the partial backordering EOQ with correlated deman...