Infinitely constrained optimization problems

Blankenship, J. W.; Falk, James E.

doi:10.1007/bf00934096

Cited by 158 publications

(169 citation statements)

References 6 publications

Supporting

Mentioning

168

Contrasting

Order By: Relevance

“…For surveys of classical methods the reader is referred to [9,10]. Particularly relevant for the proposal herein is the approach in [11]; they generate a series of candidate upper-level points by solving a relaxation of the SIP in which the constraint is imposed on a finite subset of the parameter set; the lowerlevel problem is then solved for the candidate upper-level point giving an additional lowerlevel point. By construction, this is an outer approximation and in general does not result in truly feasible points.…”

mentioning

confidence: 99%

Global optimization of generalized semi-infinite programs via restriction of the right hand side

Mitsos

Tsoukalas

2014

J Glob Optim

View full text Add to dashboard Cite

The algorithm proposed in Mitsos (Optimization 60(10-11):1291(Optimization 60(10-11): -1308(Optimization 60(10-11): , 2011 for the global optimization of semi-infinite programs is extended to the global optimization of generalized semi-infinite programs. No convexity or concavity assumptions are made. The algorithm employs convergent lower and upper bounds which are based on regular (in general nonconvex) nonlinear programs (NLP) solved by a (black-box) deterministic global NLP solver. The lower bounding procedure is based on a discretization of the lower-level host set; the set is populated with Slater points of the lower-level program that result in constraint violations of prior upper-level points visited by the lower bounding procedure. The purpose of the lower bounding procedure is only to generate a certificate of optimality; in trivial cases it can also generate a global solution point. The upper bounding procedure generates candidate optimal points; it is based on an approximation of the feasible set using a discrete restriction of the lower-level feasible set and a restriction of the right-hand side constraints (both lower and upper level). Under relatively mild assumptions, the algorithm is shown to converge finitely to a truly feasible point which is approximately optimal as established from the lower bound. Test cases from the literature are solved and the algorithm is shown to be computationally efficient.

show abstract

mentioning

confidence: 99%

Global optimization of generalized semi-infinite programs via restriction of the right hand side

Mitsos

Tsoukalas

2014

J Glob Optim

View full text Add to dashboard Cite

show abstract

“…For the infinite-dimensional problem (4.1), we will propose the iterative solution scheme, which is inspired by the discretization techniques used in semi-infinite programming [3,12]. Our solution scheme is described in the following algorithm.…”

Section: Algorithm Proceduresmentioning

confidence: 99%

A discretization iteration approach for solving a class of semivectorial bilevel programming problem

Lv¹,

Chen²

2016

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

The pessimistic optimal solution of the semivectorial bilevel programming problem with no upper level variables in the lower level constraints is concerned. Based on the scalarization techniques and optimal value transforming approach for the lower level problem, the semivectorial bilevel programming problem is transformed into the corresponding infinite-dimensional optimization problem. Then, a discretization iterative algorithm is proposed, and the convergence of the algorithm is also analyzed. The numerical results show that the algorithm is feasible for the pessimistic optimal solution of the semivectorial bilevel programming problem studied.

show abstract

“…Then if θ k − f (x k , y) can be written as a sum of squares of polynomials in y, it follows that (x k , θ k ) satisfy the semi-infinite constraints in (5). Therefore, to check the feasibility of (x k , θ k ) we need to establish whether or not there exist polynomials r i (y) such that:…”

Section: The Algorithmmentioning

confidence: 99%

An Algorithm for the Global Optimization of a Class of Continuous Minimax Problems

Parpas

Rustem

2008

J Optim Theory Appl

View full text Add to dashboard Cite

We propose an algorithm for the global optimization of continuous minimax problems involving polynomials. The method can be described as a discretization approach to the well known semi-infinite formulation of the problem. We 1 Financial support of EPSRC Grant GR/T02560/01 gratefully acknowledged. 1 proceed by approximating the infinite number of constraints using tools and techniques from semidefinite programming. We then show that under appropriate conditions the SDP approximation converges to the globally optimal solution of the problem. We also discuss the numerical performance of the method on some test problems.

show abstract

Infinitely constrained optimization problems

Cited by 158 publications

References 6 publications

Global optimization of generalized semi-infinite programs via restriction of the right hand side

Global optimization of generalized semi-infinite programs via restriction of the right hand side

A discretization iteration approach for solving a class of semivectorial bilevel programming problem

An Algorithm for the Global Optimization of a Class of Continuous Minimax Problems

Contact Info

Product

Resources

About