Feasible Method for Generalized Semi-Infinite Programming

Stein, Oliver; Winterfeld, Anton

doi:10.1007/s10957-010-9674-5

Cited by 18 publications

(7 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note also that GSIP is closely related to bilevel programs [31]; however, some of the algorithms specifically designed for bilevel programs [32,33] are not suitable for GSIPs since they allow for (small) violation of the constraint. Note also that [34] proposes a method with feasible iterates for the case of convex lower-level program.…”

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

“…However, in [36] it could be shown that a simple modification of P τ leads to inner approximations of M GSIP and thus to feasible optimal points of the approximating problems. In fact, an error analysis for the approximation of the lower-level optimal value proves that the feasible set M • τ of P • τ : min x,y 1 ,...,y p ,γ 1 ,...,…”

Section: The Outer and Inner Smoothing Reformulationsmentioning

confidence: 99%

“…A combination of the outer and inner smoothing approaches leads to 'sandwiching' procedures for M GSIP [36].…”

Section: The Outer and Inner Smoothing Reformulationsmentioning

confidence: 99%

Solving Disjunctive Optimization Problems by Generalized Semi-infinite Optimization Techniques

Kirst

Stein

2016

J Optim Theory Appl

View full text Add to dashboard Cite

We describe a new possibility to model disjunctive optimization problems as generalized semi-infinite programs. In contrast to existing methods in disjunctive programming, our approach does not expect any special formulation of the underlying logical expression. Applying existing lower-level reformulations for the corresponding semi-infinite program, we derive conjunctive nonlinear problems without any logical expressions, which can be locally solved by standard nonlinear solvers. Our preliminary numerical results on some small-scale examples indicate that our reformulation procedure is a reasonable method to solve disjunctive optimization problems.

show abstract

“…Because design centering problems are a particular instance of GSIP, this work approaches design centering problems from the perspective of and with tools from the GSIP literature (see [59] for a recent review). This approach is hardly original [58,61,72], however, bringing together these ideas in one work is useful. Further, this work compares different numerical approaches from the GSIP literature.…”

Section: Introductionmentioning

confidence: 99%

How to solve a design centering problem

Harwood

Barton

2017

Math Meth Oper Res

View full text Add to dashboard Cite

This work considers the problem of design centering. Geometrically, this can be thought of as inscribing one shape in another. Theoretical approaches and reformulations from the literature are reviewed; many of these are inspired by the literature on generalized semi-infinite programming, a generalization of design centering. However, the motivation for this work relates more to engineering applications of robust design. Consequently, the focus is on specific forms of design spaces (inscribed shapes) and the case when the constraints of the problem may be implicitly defined, such as by the solution of a system of differential equations. This causes issues for many existing approaches, and so this work proposes two restriction-based approaches for solving robust design problems that are applicable to engineering problems. Another feasible-point method from the literature is investigated as well. The details of the numerical implementations of all these methods are discussed. The discussion of these implementations in the particular setting of robust design in engineering problems is new. keywords: gsip, design centering, lower level duality, global optimization * Current version as of: May 4, 2017. This research was funded by Novartis Pharmaceuticals as part of the Novartis-MIT Center for Continuous Manufacturing.

show abstract

Feasible Method for Generalized Semi-Infinite Programming

Cited by 18 publications

References 30 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

Solving Disjunctive Optimization Problems by Generalized Semi-infinite Optimization Techniques

How to solve a design centering problem

Contact Info

Product

Resources

About