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PreprintCC BY 4.0HAL

Conditional Infimum, Hidden Convexity and S-Procedure

  • Jean-Philippe Chancelier
  • Michel de Lara
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Abstract

Detecting hidden convexity is one of the tools to address nonconvex minimization problems, and find global minimizers. We introduce the notion of conditional infimum, develop the theory, and establish a tower property, relevant for minimization problems. Then, we illustrate how the conditional infimum is instrumental in revealing hidden convexity. Thus equipped, we provide a new sufficient condition for hidden convexity in nonconvex quadratic minimization problems, that encompasses and goes beyond known results (with the notion of block-signed pair matrix-vector). We also show how the conditional infimum is especially adapted to tackle the so-called S-procedure.

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Cite

BibTeXRIS
BibTeX
@misc{chancelier2026conditional,
  title = {{Conditional Infimum, Hidden Convexity and S-Procedure}},
  author = {Jean-Philippe Chancelier and Michel de Lara},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24661},
  eprint = {2609.24661},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05754640v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Conditional Infimum, Hidden Convexity and S-Procedure
AU  - Jean-Philippe Chancelier
AU  - Michel de Lara
PY  - 2026
DA  - 2026/09/18
PB  - HAL
DO  - 10.48550/arxiv.2609.24661
UR  - https://hal.science/hal-05754640v1
AB  - Detecting hidden convexity is one of the tools to address nonconvex minimization problems, and find global minimizers. We introduce the notion of conditional infimum, develop the theory, and establish a tower property, relevant for minimization problems. Then, we illustrate how the conditional infimum is instrumental in revealing hidden convexity. Thus equipped, we provide a new sufficient condition for hidden convexity in nonconvex quadratic minimization problems, that encompasses and goes beyond known results (with the notion of block-signed pair matrix-vector). We also show how the conditional infimum is especially adapted to tackle the so-called S-procedure.
ER  -