Recent contributions to linear semi-infinite optimization: an update
نویسندگان
چکیده
منابع مشابه
An algorithm for semi-infinite polynomial optimization
We consider the semi-infinite optimization problem: f := min x∈X {f(x) : g(x,y) ≤ 0, ∀y ∈ Yx }, where f, g are polynomials and X ⊂ R as well as Yx ⊂ R , x ∈ X, are compact basic semi-algebraic sets. To approximate f we proceed in two steps. First, we use the “joint+marginal” approach of the author [9] to approximate from above the function x 7→ Φ(x) = sup{g(x,y) : y ∈ Yx} by a polynomial Φd ≥ Φ...
متن کاملComposite semi - infinite optimization
Abstract: We consider a semi-infinite optimization problem in Banach spaces, where both the objective functional and the constraint operator are compositions of convex nonsmooth mappings and differentiable mappings. We derive necessary optimality conditions for these problems. Finally, we apply these results to nonconvex stochastic optimization problems with stochastic dominance constraints, ge...
متن کاملA Comprehensive Survey of Linear Semi-infinite Optimization Theory
1 Introduction 2 Existence theorems for the LSIS 3 Geometry of the feasible set 4 Optimality 5 Duality theorems and discretizatiön 6 Stability of the LSIS 7 Stability and well-posedness of the LSIP problem 8 Optimal Solution unicity REFERENCES 3 3 5 6 10 12 14 19 23 25
متن کاملOn stable uniqueness in linear semi-infinite optimization
This paper is intended to provide conditions for the stability of the strong uniqueness of the optimal solution of a given linear semi-in nite optimization (LSIO) problem, in the sense of the maintaining of the strong uniqueness property under su¢ ciently small perturbations of all the data. We consider LSIO problems such that the family of gradients of all the constraints is unbounded, extendi...
متن کاملAn Unconstrained Convex Programming Approach to Linear Semi-Infinite Programming
In this paper, an unconstrained convex programming dual approach for solving a class of linear semi-infinite programming problems is proposed. Both primal and dual convergence results are established under some basic assumptions. Numerical examples are also included to illustrate this approach.
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ژورنال
عنوان ژورنال: Annals of Operations Research
سال: 2018
ISSN: 0254-5330,1572-9338
DOI: 10.1007/s10479-018-2987-8