If this function is sufficiently closely approximable by a polynomial or a rational function, then the semi-infinite program can be reformulated as an equivalent semidefinite program. Solving this semidefinite program is challenging if the polynomials involved are of high degree, due to numerical ...
半无穷线性规划(Semi-Infinite Linear Programming, SILP)是一种特殊的线性规划问题,它区别于标准的有限维线性规划问题,因为在约束条件中可能包含无限多个不等式约束。 具体来说,SILP 可以被描述为具有有限个变量但无限多个约束的问题。 这类问题在工程设计、经济模型以及某些物理问题中经常出现。 标准形式 SILP 的标...
4.2.1. Cone constrained programs as special cases of LSIP A cone constrained linear problem is a program of the form min c> x s:t: y :? Ax ? b 2 C; ?16? ?15? 502 ? M. Lopez, G. Still / European Journal of Operational Research 180 (2007) 491–518 where C is a closed ...
The semi-infinite programming (SIP) problem is a program with infinitely many constraints. It can be reformulated as a nonsmooth nonlinear programming prob... C Ling,LQ Qi,GL Zhou,... - 《Journal of Optimization Theory & Applications》 被引量: 50发表: 2006年 FIR filter design in the compl...
In Mitsos (Optimization 60(10–11):1291–1308, 2011), it is claimed that a modification of this lower bounding method involving approximate solution of the lower-level program yields convergent lower bounds. We show with a counterexample that this claim is false, and discuss what kind of ...
Weak and strong duality results and the optimality results of relative saddlepoint program are given for a class of generalized nonlinear semi-infinite generalized fractional programming. 利用Ben-Tal广义代数运算,进一步推广了凸性,定义了(h,φ)-η半连通集,(h,φ)-η半预不变凸函数、(h,φ)-η半预...
∑i=1kwi=1θ2∗=argmaxθ2∈Θ2−∫X[ηt(x)−η2(x,θ2)]2ξ(dx), showing that the T-optimality criterion can be equivalently viewed as a maximin, a minimax or a bilevel optimization problem with the outer program having convex properties and the inner problem being concave or...
The semi-infinite programming (SIP) problem is a program with infinitely many constraints. It can be reformulated as a nonsmooth nonlinear programming problem with finite constraints by using an integral function. Due to the nondifferentiability of the integral function, gradient-based algorithms cannot...
Pereira, A., Costa, M., Fernandes, E.: Interior point filter method for semi-infinite program- ming problems. Optimization 60, 1309-1338 (2011)Pereira, A.I., Costa, M.F.P., Fernandes, E.M.G.P.: Interior point filter method for semi-infinite programming problems, Optimization, 60(10...
the (SIP) stems from the min-max program (13) with \(q : \mathcal {X} \times \mathcal {Y} \rightarrow {\mathbb {R}}\) and q being coercive in \(\varvec{x}\) for all \(\varvec{y}\). In this case, we consider in the following the epigraph reformulation of this min...