A derivative-free 𝒱𝒰-algorithm for convex finite-max problems

Hare, Warren; Planiden, Chayne; Sagastizábal, Claudia

doi:10.1080/10556788.2019.1668944

Cited by 11 publications

(6 citation statements)

References 52 publications

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“…Objectives of the form (5.9) are also addressed by Hare, Planiden and Sagastizábal (2019), who develop an algorithm that decomposes such problems into orthogonal subspaces associated with directions of non-smoothness and directions of smoothness. The resulting derivative-free -algorithm employs model-based estimates of gradients to form and update this decomposition (Hare 2014).…”

Section: Methods For Structured Objectivesmentioning

confidence: 99%

Derivative-free optimization methods

2019

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Dedicated to the memory of Andrew R. Conn for his inspiring enthusiasm and his many contributions to the renaissance of derivative-free optimization methods. AbstractIn many optimization problems arising from scientific, engineering and artificial intelligence applications, objective and constraint functions are available only as the output of a black-box or simulation oracle that does not provide derivative information. Such settings necessitate the use of methods for derivative-free, or zeroth-order, optimization. We provide a review and perspectives on developments in these methods, with an emphasis on highlighting recent developments and on unifying treatment of such problems in the non-linear optimization and machine learning literature. We categorize methods based on assumed properties of the black-box functions, as well as features of the methods. We first overview the primary setting of deterministic methods applied to unconstrained, non-convex optimization problems where the objective function is defined by a deterministic black-box oracle. We then discuss developments in randomized methods, methods that assume some additional structure about the objective (including convexity, separability and general non-smooth compositions), methods for problems where the output of the black-box oracle is stochastic, and methods for handling different types of constraints.

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Section: Methods For Structured Objectivesmentioning

confidence: 99%

Derivative-free optimization methods

2019

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“…For instance, they are frequently used as penalty functions, such as • p , and max(•, 0) p (an exact penalty for inequality constraints). Thus, in the literature one sometimes sees treatments of particular convex functions h. For example, in [11,55] h is fixed as • 2 2 , while in [27,44,56] h is fixed as max(•). In [22,58], h is fixed as a polyhedral convex function, which is a convex piecewise-affine function.…”

Section: Literature Reviewmentioning

confidence: 99%

“…, where the first inequality comes from (11b), the second inequality comes from (27), the third inequality comes from Assumption 1.B and Assumption 2.D and the last inequality comes from Assumption 2.C, Assumption 3,and (25).…”

Section: Linementioning

confidence: 99%

Manifold Sampling for Optimizing Nonsmooth Nonconvex Compositions

Larson,

Menickelly,

Zhou

2020

Preprint

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We propose a manifold sampling algorithm for minimizing a nonsmooth composition f = h • F , where we assume h is nonsmooth and may be inexpensively computed in closed form and F is smooth but its Jacobian may not be available. We additionally assume that the composition h • F defines a continuous selection. Manifold sampling algorithms can be classified as model-based derivative-free methods, in that models of F are combined with particularly sampled information about h to yield local models for use within a trust-region framework. We demonstrate that cluster points of the sequence of iterates generated by the manifold sampling algorithm are Clarke stationary. We consider the tractability of three particular subproblems generated by the manifold sampling algorithm and the extent to which inexact solutions to these subproblems may be tolerated. Numerical results demonstrate that manifold sampling as a derivative-free algorithm is competitive with state-of-the-art algorithms for nonsmooth optimization that utilize first-order information about f .

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“…Algoritma look-up table dilakukan dengan memasukan kata-kata ke database secara manual. Ketika pengguna memasukan kata infleksi (perubahan bentuk kata yang tidak mengubah arti kata tersebut), maka stemmer akan mencari keberadaan [12]. Gamabar.…”

Section: Metode Penelitianunclassified

Analisa Modifikasi Algoritma Stemming Untuk Kasus Overstemming

Hersianie

2020

teknokom

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Overstemming merupakan pemenggalan kata ke bentuk asal (root word) yang berlebihan. Hal ini menyebabkan kata tersebut bermakna sangat berbeda dengan kata asal. Namun, stem yang dihasilkan sama bentuknya. Untuk mengatasi permasalahan tersebut, penelitian sebelumnya telah menerapkan algoritma stemming dengan tabel aturan kata. Namun kekurangan dari tabel aturan kata ini adalah kesulitan dalam menambahkan jenis kata yang mengalami overstemming. Oleh karena itu, penelitian ini bertujuan untuk memodifikasi algoritma overstemming tersebut. Penelitian ini akan menggabungkan algoritma stemming (hybrid stemming) yaitu algoritma look-up table, tabel aturan kata dan algoritma stemming Porter yang biasa digunakan. Dataset yang digunakan dalam pengujian adalah atribut judul pada dokumen publikasi ilmiah. Hasil pengujian menunjukkan bahwa modifikasi algoritma stemming menghasilkan recall sebesar 89, 9%.Saran untuk penelitian selanjutnya adalah pengujian dapat dilakukan menggunakan atribut lainnnya pada dokumen publikasi.

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A derivative-free 𝒱𝒰-algorithm for convex finite-max problems

Cited by 11 publications

References 52 publications

Derivative-free optimization methods

Derivative-free optimization methods

Manifold Sampling for Optimizing Nonsmooth Nonconvex Compositions

Analisa Modifikasi Algoritma Stemming Untuk Kasus Overstemming

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