Pure Cutting‐Plane Algorithms and their Convergence

Gade, Dinakar; Küçükyavuz, Simge

doi:10.1002/9780470400531.eorms1084

Cited by 2 publications

(2 citation statements)

References 42 publications

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“…It is well-known that ILP problems can be solved with a finite number of steps, for example, by the cuttingplane algorithm [22,23]. Therefore, by combining the ILP problem above with the cost updating presented previously, we can get an E-optimal code forest within a finite number of steps.…”

Section: Integer Programming Formulationmentioning

confidence: 99%

General Form of Almost Instantaneous Fixed-to-Variable-Length Codes

Sugiura,

Kamamoto,

Moriya

2023

IEEE Trans. Inform. Theory

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This paper presents an optimal construction of N -bit-delay almost instantaneous fixed-to-variable-length (AIFV) codes, the general form of binary codes we can make when finite bits of decoding delay are allowed. The presented method enables us to optimize lossless codes among a broader class of codes compared to the conventional FV and AIFV codes. The paper first discusses the problem of code construction, which contains some essential partial problems, and defines three classes of optimality to clarify how far we can solve the problems. The properties of the optimal codes are analyzed theoretically, showing the sufficient conditions for achieving the optimum. Then, we propose an algorithm for constructing N -bit-delay AIFV codes for given stationary memory-less sources. The optimality of the constructed codes is discussed both theoretically and empirically. They showed shorter expected code lengths when N ≥ 3 than the conventional AIFV-m and extended Huffman codes. Moreover, in the random numbers simulation, they performed higher compression efficiency than the 32-bit-precision range codes under reasonable conditions.

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Section: Integer Programming Formulationmentioning

confidence: 99%

General Form of Almost Instantaneous Fixed-to-Variable-Length Codes

Sugiura,

Kamamoto,

Moriya

2023

IEEE Trans. Inform. Theory

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“…Similarly, pure cutting plane algorithms using disjunctive cutting planes do not converge finitely for deterministic MIPs with both continuous and general integer variables. (See [21] for a review of pure cutting plane algorithms and their convergence for deterministic MIPs.) Hence, it does not seem possible to immediately extend the decomposition algorithms of [22,54,68] to problems that contain both continuous and general integer variables in the first and second stages.…”

Section: General Integer First and Secondmentioning

confidence: 99%

An Introduction to Two-Stage Stochastic Mixed-Integer Programming

Küçükyavuz

Sen

2017

The Operations Research Revolution

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This paper provides an introduction to algorithms for two-stage stochastic mixed-integer programs. Our focus is on methods which decompose the problem by scenarios representing randomness in the problem data. The design of these algorithms depend on where the uncertainty appears (right-hand-side, recourse matrix and/or technology matrix) and where the continuous and discrete decision variables are (first-stage and/or secondstage). In addition we provide computational evidence that, similar to other classes of stochastic programming problems, decomposition methods can provide desirable theoretical properties (such as finite convergence) as well as enhanced computational performance when compared to solving a deterministic equivalent formulation using an advanced commercial MIP solver.

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Pure Cutting‐Plane Algorithms and their Convergence

Cited by 2 publications

References 42 publications

General Form of Almost Instantaneous Fixed-to-Variable-Length Codes

General Form of Almost Instantaneous Fixed-to-Variable-Length Codes

An Introduction to Two-Stage Stochastic Mixed-Integer Programming

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