Following a few words on multifunctions in the mathematical literature, a very brief recall on dual spaces, some preliminary notations and definitions in the introduction, we give some results on those functions in the second paragraph. In the third paragraph, a duality theory in...

Idle land remains to be an issue that warrants further investigation. This study aspires to unveil the economic potential of idle land which is cultivated with a combination of cash crops -- vegetables and fruits by young enterprising individuals. Linear programming is employed to derive optimal...

With the growing concerns about worldwide energy and environmental sustainability, heat pump water heaters and solar water heaters became popular in China after 2000. The combinations between the heat pump air conditioner, heat pump water heater and solar water heater brought about more energy...

Page and Wooders (1996) prove that the no-unbounded-arbitrage (NUBA) condition introduced by Page (1987) is equivalent to the existence of a no arbitrage price (NAPS) when no agent has non-null useless vectors. Al- louch, Le Van and Page (2002) show that their generalized NAPS condition is...

In dose-response studies, the dose range is often restricted due to concerns over drug toxicity and/or efficacy. We derive optimal designs for estimating the underlying dose-response curve for a restricted or unrestricted dose range with respect to a broad class of optimality criteria. The...

In solving certain optimization problems, the corresponding Lagrangian dual problem is often solved simply because in these problems the dual problem is easier to solve than the original primal problem. Another reason for their solution is the implication of the weak duality theorem which...

In this paper, we propose, analyze and test primal and dual versions of the alternating direction algorithm for the sparse signal reconstruction from its major noise contained observation data. The algorithm minimizes a convex non-smooth function consisting of the sum of ℓ <Subscript>1</Subscript>-norm...</subscript>