LetZ be a compact set of the real space ℜ with at leastn + 2 points;f,h1,h2:Z → ℜ continuous functions,h1,h2 strictly positive andP(x,z),x≔(x 0 ,...,x n ) τ ε ℜ n+1 ,z ε ℜ, a polynomial of degree at mostn. Consider a feasible setM ≔ {x ε ℜ n+1 ∣∀z εZ, −h 2 (z) ≤P(x,...

For semi-infinite programming (SIP), we consider a class of smoothed penalty functions, which approximate the exact $$l_\rho (0\rho \le 1)$$ penalty functions. On base of the smoothed penalty function, we present a feasible penalty algorithm for solving SIP. Without any boundedness condition or...

We consider the problem of valuing European options in a complete market but with incomplete data. Typically, when the underlying asset dynamics is not specified, the martingale probability measure is unknown. Given a consensus on the actual distribution of the underlying price at maturity, we...

The second-order cone program (SOCP) is an optimization problem with second-order cone (SOC) constraints and has achieved notable developments in the last decade. The classical semi-infinite program (SIP) is represented with infinitely many inequality constraints, and has been studied...

In this paper we study the (Berge) upper semicontinuity of a generic multifunction assigning to each parameter, in a metric space, a closed convex subset of the n-dimensional Euclidean space. A relevant particular case arises when we consider the feasible set mapping associated with a parametric...

We give a generic regularity condition under which each weakly efficient decision making unit in the CCR model of data envelopment analysis is also CCR-efficient. Then we interpret the problem of finding maximal parameters which preserve efficiency of CCR-efficient DMUs under directional...

When the exact unbiasedness condition is relaxed to a near unbiasedness condition, this short communication shows that the best linear near unbiased estimation problem is actually a semi-infinite programming problem. Our recently developed dual parameterization method is applied for solving the...