A new polynomial-time algorithm for linear programming.

Karmarkar, N. (1984). A new polynomial-time algorithm for linear programming. Combinatorica, 4(4), 373-395.

Type

Journal article

Intellectual base

Primary research

Year

1984

Volume

4

Issue

4

Pages

373-395

Link

https://www.stat.uchicago.edu/~lekheng/courses/302/classics/karmarkar.pdf

Cited from

operations_research

Cited by

4 citations across 4 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Linear Programming (LP)
  • The extensions increase complexity but have been absorbed into standard industry practice.

    This source(Interior-point method; practical polynomial-time LP solution.)

• Resource Management

  • This source(Interior-point method; practical polynomial-time LP solution.)

Domain-specific

• Interior
  • Interior-point methods in convex optimization (Karmarkar, 1984; logarithmic-barrier and primal-dual methods) navigate the interior of the feasible region rather than traversing its boundary as simplex methods do, achieving polynomial-time complexity for linear programming

    Supported in partVerified against the publisher's abstract

    “We present a new polynomial-time algorithm for linear programming.”

    Read by an automated reader; not a human review. How support was checked

• Interior-Point Method
  • Karmarkar's original linear-programming algorithm projectively recenters a strictly interior point and moves from it; the later barrier/path-following family uses a smooth barrier to represent inequality boundaries during optimization.

Verification

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