Technical Note—Sharper Bounds on Nonconvex Programs
نویسندگان
چکیده
منابع مشابه
A Note on Error Bounds for Convex and Nonconvex Programs
Given a single feasible solution xF and a single infeasible solution xI of a mathematical program, we provide an upper bound to the optimal dual value. We assume that xF satisfies a weakened form of the Slater condition. We apply the bound to convex programs and we discuss its relation to Hoffman-like bounds. As a special case, we recover a bound due to Mangasarian [11] on the distance of a poi...
متن کاملA Note on Error Bounds For1 Convex and Nonconvex Programs
Given a single feasible solution xF and a single infeasible solution xI of a mathematical program, we provide an upper bound to the optimal dual value. We assume that xF satisfies a weakened form of the Slater condition. We apply the bound to convex programs and we discuss its relation to Hoffman-like bounds. As a special case, we recover a bound due to Mangasarian [Man97] on the distance of a ...
متن کاملEigenvalue techniques for proving bounds for convex objective, nonconvex programs
• F (x) is a convex quadratic, i.e. F (x) = xTMx + vTx (with M 0 and v ∈ Rn). • P ⊆ Rn is a convex set over which we can efficiently optimize F , • K ⊆ Rn is a non-convex set with “special structure”. • Typically, n could be quite large. A standard approach to solving this problem would start by solving a convex relaxation to F , thereby obtaining a lower bound on F z. However, when K is comple...
متن کاملBounds on the Minimizers of (nonconvex) Regularized Least-Squares
This is a theoretical study on the minimizers of cost-functions composed of an `2 data-fidelity term and a possibly nonsmooth or nonconvex regularization term acting on the differences or the discrete gradients of the image or the signal to restore. More precisely, we derive general nonasymptotic analytical bounds characterizing the local and the global minimizers of these cost-functions. We fi...
متن کاملConvergent LMI relaxations for nonconvex quadratic programs
We consider the general nonconvex quadratic programming problem and provide a series of convex positive semidefinite programs (or LMI relaxations) whose sequence of optimal values is monotone and converges to the optimal value of the original problem. It improves and includes as a special case the well-known Shor’s LMI formulation. Often, the optimal value is obtained at some particular early r...
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: Operations Research
سال: 1974
ISSN: 0030-364X,1526-5463
DOI: 10.1287/opre.22.2.410