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Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming
Abstract
This note formulates a convex mathematical programming problem in which the usual definition of the feasible region is replaced by a significantly different strategy. Instead of specifying the feasible region by a set of convex inequalities, f i(x) ≦ b i, i = 1, 2, …, m, the feasible region is defined via set containment. Here n convex activity sets {K j, j = 1, 2, …, n} and a convex resource set K are specified and the feasible region is given by [Formula: see text] where the binary operation + refers to addition of sets. The problem is then to find x̄ ∈ X that maximizes the linear function c · x. When the resource set has a special form, this problem is solved via an auxiliary linear-programming problem and application to inexact linear programming is possible.
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Cited by
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Metadata
- Authors
- Soyster, A. L.
- Venue
- Operations Research
- Published
- 1973-10
- Volume
- 21
- Issue
- 5
- Pages
- 1154-1157
- ISSN
- 0030-364X (ISSN-L)
- 1526-5463
- OpenAlex
- W1990275757
- Cited by
- 1,822
- References
- 0
- FWCI
- 0.43
- Type
- journal article
- Language
- en
- Open access
- closed
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