Mathematica(@mathemetica):Every local minimum is global. When both the objective and the feasible set are convex, a point that cannot be improved in any neighborhood cannot be improved anywhere. The geometry itself forbids hidden valleys; first-order stationarity is already optimality. The same fact, isolated in the study of convex bodies around 1900, is why linear programs, positive-semidefinite quadratic programs, and a wide family of modern learning problems can be solved to proven global optimality.

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Mathematica@mathemetica

2026.09.22 23:36

Every local minimum is global. When both the objective and the feasible set are convex, a point that cannot be improved in any neighborhood cannot be improved anywhere. The geometry itself forbids hidden valleys; first-order stationarity is already optimality. The same fact, isolated in the study of convex bodies around 1900, is why linear programs, positive-semidefinite quadratic programs, and a wide family of modern learning problems can be solved to proven global optimality.