Conditions for Exact Convex Relaxation and No Spurious Local Optima
نویسندگان
چکیده
Nonconvex optimization problems can be approximately solved via relaxation or local algorithms. For many practical such as optimal power flow (OPF) problems, both approaches tend to succeed in the sense that is usually exact and algorithms converge a global optimum. In this article, we study conditions are sufficient necessary for nonconvex simultaneously have no spurious optima. These help explain widespread empirical experience OPF even though computationally hard theory, seem easy practice.
منابع مشابه
Matrix Completion has No Spurious Local Minimum
Matrix completion is a basic machine learning problem that has wide applications, especially in collaborative filtering and recommender systems. Simple non-convex optimization algorithms are popular and effective in practice. Despite recent progress in proving various non-convex algorithms converge from a good initial point, it remains unclear why random or arbitrary initialization suffices in ...
متن کاملno-homomorphism conditions for hypergraphs
In this paper, we define some new homomorphism-monotone parameters for hypergraphs. Using these parameters, we extend some graph homomorphism results to hypergraph case. Also, we present some bounds for some well-known invariants of hypergraphs such as fractional chromatic number,independent numer and some other invariants of hyergraphs, in terms of these parameters.
متن کاملLocal optima smoothing for global optimization
It is widely believed that in order to solve large scale global optimization problems an appropriate mixture of local approximation and global exploration is necessary. Local approximation, if first order information on the objective function is available, is efficiently performed by means of local optimization methods. Unfortunately, global exploration, in absence of some kind of global inform...
متن کاملExact Boundary Conditions for Periodic Waveguides Containing a Local Perturbation
We consider the solution of the Helmholtz equation−∆u(x)−n(x)ωu(x) = f(x), x = (x, y), in a domain Ω which is infinite in x and bounded in y. We assume that f(x) is supported in Ω := {x ∈ Ω |a− < x < a} and that n(x) is x-periodic in Ω\Ω. We show how to obtain exact boundary conditions on the vertical segments, Γ− := {x ∈ Ω |x = a−} and Γ := {x ∈ Ω |x = a}, that will enable us to find the solut...
متن کاملCharacterizing Local Optima for Maximum Parsimony.
Finding the best phylogenetic tree under the maximum parsimony optimality criterion is computationally difficult. We quantify the occurrence of such optima for well-behaved sets of data. When nearest neighbor interchange operations are used, multiple local optima can occur even for "perfect" sequence data, which results in hill-climbing searches that never reach a global optimum. In contrast, w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Transactions on Control of Network Systems
سال: 2022
ISSN: ['2325-5870', '2372-2533']
DOI: https://doi.org/10.1109/tcns.2021.3112758