Optimization is a fundamental pillar of scientific and technological progress. It provides the mathematical framework for making the best decisions under constraints - across engineering, economics, data science, and beyond. In particular, many real-world optimization problems are nonconvex, making them especially difficult to solve efficiently and reliably. DC (Difference of Convex functions) programming and DCA (DC Algorithm), developed 40 years ago, have emerged as a powerful and versatile method for tackling such nonconvex problems. By exploiting hidden convexity through DC decompositions, DCA offers a unifying and effective framework for the challenging nonconvex optimization tasks.

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DC Programming and DCA: 40 Years of Breakthroughs Driving Intelligence and Technology

  • Hoai An Le Thi,
  • Tao Pham Dinh

摘要

Optimization is a fundamental pillar of scientific and technological progress. It provides the mathematical framework for making the best decisions under constraints - across engineering, economics, data science, and beyond. In particular, many real-world optimization problems are nonconvex, making them especially difficult to solve efficiently and reliably. DC (Difference of Convex functions) programming and DCA (DC Algorithm), developed 40 years ago, have emerged as a powerful and versatile method for tackling such nonconvex problems. By exploiting hidden convexity through DC decompositions, DCA offers a unifying and effective framework for the challenging nonconvex optimization tasks.