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Operations Research, 2006 The well-known and established global optimality conditions based on the Lagrangian formulation of an optimization problem are consistent if and only if the duality gap is zero.
Torbjörn Larsson, Michael Patriksson
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On Global Optimality Conditions for Nonlinear Optimal Control Problems
Journal of Global Optimization, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Francis H. Clarke +2 more
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Journal of Optimization Theory and Applications, 2007 We present sufficient conditions for the global optimality of bivalent nonconvex quadratic programs involving quadratic inequality constraints as well as equality constraints.
V Jeyakumar, A M Rubinov, Wu Z Y
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Global Optimality Conditions in Nonconvex Optimization
Journal of Optimization Theory and Applications, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Global Optimality Conditions for Nonconvex Optimization
Journal of Global Optimization, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Conditions for Global Optimality 2
Journal of Global Optimization, 1998In this paper bearing the same title as our earlier survey-paper [11] we pursue the goal of characterizing the global solutions of an optimization problem, i.e. getting at necessary and sufficient conditions for a feasible point to be a global minimizer (or maximizer) of the objective function.
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A Sufficient Condition for Local Optima to be Globally Optimal
2020 59th IEEE Conference on Decision and Control (CDC), 2020Consider an optimization problem with a convex cost function but a non-convex compact feasible set $\mathcal{X}$, and its relaxation with a compact and convex feasible set $\hat {\mathcal{X}} \supset \mathcal{X}$. We prove that if from any point $x \in \hat {\mathcal{X}}\backslash \mathcal{X}$ there is a path connecting x to $\mathcal{X}$ along which ...
Zhou, Fengyu, Low, Steven H.
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Global Optimality Conditions for Quadratic Optimization Problems with Binary Constraints
SIAM Journal on Optimization, 2000Summary: We consider nonconvex quadratic optimization problems with binary constraints. Our main result identifies a class of quadratic problems for which a given feasible point is global optimal. We also establish a necessary global optimality condition. These conditions are expressed in a simple way in terms of the problem's data.
Amir Beck, Marc Teboulle
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Global optimality conditions and exact penalization
Optimization Letters, 2017The author considers nonconvex optimization problems with inequality constraints. Both the objective function and the functions occuring in the constraints are d.-c. functions, i.e., they are expressed as the difference of two convex functions. All functions of the problems are differentiable. It is further assumed that the set of feasible solutions is
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On Global Optimality Conditions via Separation Functions
Journal of Optimization Theory and Applications, 2001This paper examines some axiomatic definitions of separation functions that can be employed fruitfully in the analysis of side-constrained extremum problems. A study of their general properties points out connections with abstract convex analysis and recent generalizations of Lagrangian approaches to duality and exact penalty methods.
Rubinov, AM, UDERZO, AMOS
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