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All Journal Jurnal Matematika dan Statistika serta Aplikasinya (Jurnal MSA) Journal of Natural Sciences and Mathematics Research DIDAKTIKA : Jurnal Kependidikan Musamus Journal of Mathematics Education Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika Square : Journal of Mathematics and Mathematics Education LOSARI: Jurnal Pengabdian Kepada Masyarakat ARRUS Journal of Mathematics and Applied Science Journal of Mathematics: Theory and Applications Mestaka: Jurnal Pengabdian Kepada Masyarakat ARRUS Jurnal Pengabdian Kepada Masyarakat Jurnal Hasil-Hasil Pengabdian dan Pemberdayaan Masyarakat (JHP2M) SMART: Jurnal Pengabdian Kepada Masyarakat Semeton Mathematics Journal
Syamsuddin Mas'ud
Universitas Negeri Makassar
Agriculture, Biological Sciences & Forestry Humanities Biochemistry, Genetics & Molecular Biology Chemistry Computer Science & IT Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Energy Environmental Science Health Professions Languange, Linguistic, Communication & Media Library & Information Science Materials Science & Nanotechnology Mathematics Mechanical Engineering Medicine & Pharmacology Physics Public Health Social Sciences Transportation Other

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Journal : Semeton Mathematics Journal

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Sejarah dan Definisi Klasik Fungsi Konveks Mas'ud, Syamsuddin
Semeton Mathematics Journal Vol 2 No 1 (2025): April
Publisher : Program Studi Matematika

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/semeton.v2i1.282

Abstract

The concept of convexity is a fundamental pillar in optimization theory and inequality analysis. This article aims to review the history and classical definition of convex functions through a literature-based approach. The literature reviewed includes works by Jensen [1], Rockafellar [2], Boyd & Vandenberghe [3], and Niculescu & Persson [4]. The analysis highlights the connection between the geometric definition of convex functions and Jensen's inequality, which demonstrates the consistency of inequality structures in both deterministic and probabilistic contexts. This study emphasizes that Jensen's inequality not only extends the concept of convex functions in probability theory but also strengthens the understanding of its geometric definition in classical analysis. This article is intended to serve as an introduction for students and researchers wishing to comprehend the foundational structure of convexity in modern mathematical theory.
Optimisasi Linear dan Kuadratik: Tinjauan Literatur Mas'ud, Syamsuddin
Semeton Mathematics Journal Vol 2 No 2 (2025): Oktober
Publisher : Program Studi Matematika

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/semeton.v2i2.284

Abstract

Convex Optimization plays a crucial role in various scientific and industrial applications, such as economics, engineering, and computer science, with a primary focus on linear and quadratic optimization. This study examines the characteristics and comparison between linear and quadratic optimization, two main subclasses of convex optimization. Linear optimization (LP) is characterized by a linear objective function and linear constraints, where classical methods such as Simplex and Interior-Point are used for efficient solutions. In contrast, quadratic optimization (QP) involves a convex quadratic objective function with linear constraints, requiring more complex methods such as Karush-Kuhn-Tucker (KKT) factorization, Schur-Complement, Null-Space, Active-Set, and Interior-Point for solving. This paper summarizes various solution methods for both types of optimizations and compares their strengths and limitations. The key findings indicate that linear optimization is simpler and more efficient, while quadratic optimization offers greater flexibility in modeling problems with more complex structures. The study concludes that a deep understanding of both approaches is essential for the development of more efficient and applicable convex optimization algorithms.
Co-Authors Ahmad Ansar ANDIKA SAPUTRA Andika Saputra Hisyam Ihsan Izzulhaq, Agung Ja'faruddin, Ja'faruddin Oeitama, Whannie Youngger Oeitama, Whennie Youngger Rahmat Syam Ramadana, Yusuf Sitandi, Flora Frisilia Sukarna Syahrullah Asyari, Syahrullah Tampa, Alimuddin Wahidin Ashari, Nur Yusuf Ramadana Zaidulkhair Hamzi