9 problems

Full stability excludes critical multipliers in extended nonlinear programs
arXiv@arxiv
Consider an extended nonlinear program with local minimizers and associated Lagrange multipliers. A local minimizer is fully stable when it has the stability property defined in th…
Conjectureopenlagrange-multipliers nonlinear-optimization stability
0
Powell's convergence conjecture under linearly growing Hessian approximations
arXiv@arxiv
Powell's convergence conjecture. Convergence continues to hold under this weaker assumption.
Conjectureopennonlinear-optimization trust-region-methods
0
Power variation conjecture for nonlinear conjugate gradient restart conditions
arXiv@arxiv
Let the restart condition for a nonlinear conjugate gradient method involve a right-hand side containing a power, as in the condition discussed in the paper. Power variation conjec…
Conjectureopenconjugate-gradient-methods nonlinear-optimization
0
Two-boundary-condition solvability conjecture for nonlinear acousto-electric tomography reconstruction
arXiv@arxiv
Consider the non-linear reconstruction problem in acousto-electric tomography, with properly chosen boundary conditions. Two-boundary-condition solvability conjecture. The non-line…
Conjectureopenacousto-electric-tomography inverse-problems nonlinear-optimization
0
Two-boundary-condition uniqueness conjecture for two-dimensional acousto-electric tomography
arXiv@arxiv
Let the conductivity satisfy $\sigma\in H^s(\Omega)$ , where $s>\frac{n}{2}$ is an integer, and consider the two-dimensional problem with $m=2$ boundary conditions satisfying the de…
Conjectureopenacousto-electric-tomography inverse-problems nonlinear-optimization
0
The rank-plus-one conjecture for second-order optimality under MFCQ
arXiv@arxiv
The rank-plus-one conjecture for second-order optimality. If $x^*$ is a local minimizer, MFCQ holds at $x^*$ , and the rank of…
Conjectureopenaugmented-lagrangian-methods nonlinear-optimization optimality-conditions
0
The rank-one Jacobian increase conjecture for nonlinear optimization
arXiv@arxiv
Rank-one Jacobian increase conjecture. Under these assumptions, the optimality condition stated in the source holds with the cone $K$ equal to the lineality space of $C(x^*)$ .
Conjectureopenconstraint-qualifications nonlinear-optimization
0
Approximate AC power-flow feasibility is in NP
arXiv@arxiv
Consider an approximate version of the lossless AC power-flow feasibility system in which the equation … is replaced by … where $\epsilon>0$ is part of the input. Approximate feasi…
Conjectureopencomputational-complexity nonlinear-optimization power-systems
2
CSDP tightness conjecture for quadratic transformation bounds
arXiv@arxiv
For matrices $A_1,\ldots,A_m$ and the associated nonlinear eigenvalue optimization problem … let the proposed convex semidefinite programming (CSDP) relaxation be the resulting upp…
Conjectureopennonlinear-optimization quadratic-transformations semidefinite-programming
0