[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-956197","data":"\u003Cdiv class=\u0022container content-rte\u0022\u003E\n  \u003Cdiv class=\u0022row\u0022\u003E\n    \u003Cdiv class=\u0022box col-md-6 bg-primary text-white\u0022\u003E\n      \u003Ch2 class=\u0022h1 text-left\u0022\u003E  Convex Optimization\n\u003C\/h2\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EECTS :\n          2.5\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ESemestre calendaire :\n          Semester 2\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ED\u00e9tail du volume horaire\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ECours magistraux :\u003C\/span\u003E\n                                      \u003Cspan\u003E12\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                              \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ETravaux dirig\u00e9s :\u003C\/span\u003E\n                                      \u003Cspan\u003E12\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                                            \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ELangue d\u0026#039;enseignement\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EAnglais\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EEnseignement \u00e0 distance\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003Enon\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n    \u003Cdiv class=\u0022box col-md-6\u0022\u003E\n                    \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EProgramme \/ plan \/ contenus\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EConvex optimization has emerged as a critical tool for quantum information scientists, leveraging the natural convexity of quantum theory to offer powerful techniques for solving a variety of complex problems in the field. In this course we will develop these tools, with a focus on semidefinite optimization, analysing their mathematical properties and discussing their practical usage. The course will be driven by applications throughout quantum information science, using the tools we develop to solve important problems and provide new powerful perspectives on the field.\u003C\/p\u003E\n\u003Cp\u003E\u003Cstrong\u003EPlan of the course.\u003C\/strong\u003E\u003C\/p\u003E\n\u003Cp\u003ELecture 1 (Convexity and convex optimisation)\u003C\/p\u003E\n\u003Cp\u003EConvex sets, cones and functions. Convex optimization problems and their properties.\u003C\/p\u003E\n\u003Cp\u003ELecture 2 (Linear, semidefinite and conic optimisation)\u003C\/p\u003E\n\u003Cp\u003ESimple examples. Duality, Slater\u0027s theorem, Complementary slackness. Practical considerations and symmetries.\u003C\/p\u003E\n\u003Cp\u003ELecture 3 (Basic applications to quantum theory)\u003C\/p\u003E\n\u003Cp\u003EApplications to: discrimination tasks, entanglement witnessing, cloning machines, complexity theory, channel coding.\u003C\/p\u003E\n\u003Cp\u003ELecture 4 (The DPS hierarchy)\u003C\/p\u003E\n\u003Cp\u003EThe separability problem and the DPS hierarchy. De finetti theorem. Applications.\u003C\/p\u003E\n\u003Cp\u003ELecture 5-6 (SDPs as proof tools)\u003C\/p\u003E\n\u003Cp\u003ESemidefinite representability of functions. Applications to proving properties of trace norm, fidelity and entropies. Additivity, data processing, inequalities.\u003C\/p\u003E\n\u003Cp\u003ELecture 7 (Noncommutative polynomial optimization)\u003C\/p\u003E\n\u003Cp\u003EBasic problem, semidefinite hierarchy solution.\u0026nbsp; Applications to Bell-nonlocality, cryptography, ground state energy problem.\u003C\/p\u003E\n\u003Cp\u003ELecture 8 (Sum of squares).\u003C\/p\u003E\n\u003Cp\u003ESum of Hermtian squares polynomials, properties, duality to NCPOPs, applications.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n                                                \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ENature de l\u0026#039;\u00e9valuation\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EEvaluation Continue non Int\u00e9grale\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n  \u003C\/div\u003E\n\u003C\/div\u003E\n","settings":null}]