Results 261 to 270 of about 32,948 (308)

Optimality conditions for global optimization (I)

Acta Mathematicae Applicatae Sinica, 1985
With the help of the theory of measure and integration several global optimality conditions, which are sufficient and necessary, are given for minimizing a continuous function over a topological space.
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OPTIMALITY CONDITIONS AND APPROXIMATE OPTIMALITY CONDITIONS IN LOCALLY LIPSCHITZ VECTOR OPTIMIZATION

Optimization, 2002
Abstract In this paper, we study constrained locally Lipschitz vector optimization problems in which the objective and constraint spaces are Hilbert spaces, the decision space is a Banach space, the dominating cone and the constraint cone may be with empty interior. Necessary optimality conditions for this type of optimization problems are derived.
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On Sufficient Conditions in Nonsmooth Optimization

Mathematics of Operations Research, 1982
Second-order conditions are given which are sufficient for a point to be a local minimizer for certain nonlinear programming problems defined on Banach spaces. The functions involved in the problems are not required to be smooth or convex; indeed, they are required only to satisfy certain conditions which are weak enough to be satisfied by all locally
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Condition Number Theorems in Optimization

SIAM Journal on Optimization, 2003
Summary: Condition numbers for optimization problems in Banach spaces are considered. Lower and upper estimates of the (suitably defined) distance from ill-conditioning are obtained in terms of the reciprocal of condition numbers. An approach is presented based on the metric regularity of the inverse to the arg min map.
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Necessary Conditions in Nonsmooth Optimization

Mathematics of Operations Research, 1984
The paper contains four theorems concerning first order necessary conditions for a minimum in nonsmooth optimization problems in Banach spaces: a Lagrange multiplier rule for a mathematical programming problem in which an infinite dimensional equality constraint is included in the constraints, a general maximum principle for nonsmooth optimal control ...
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Necessary Optimality Conditions in Multiobjective Dynamic Optimization

SIAM Journal on Control and Optimization, 2004
Let \(F: [a,b] \times \mathbb{R}^n \multimap \mathbb{R}^n\) be a closed-valued multimap, measurable in the first argument and sub-Lipschitzean in the second one; \(S \subset \mathbb{R}^n \times \mathbb{R}^n\) a nonempty closed set and \(f: \mathbb{R}^n \times \mathbb{R}^n \rightarrow \mathbb{R}^m\) a map. Extending the result of \textit{A.
Saïd Bellaassali, Abderrahim Jourani
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Optimality Conditions for Simultaneous Topology and Shape Optimization

SIAM Journal on Control and Optimization, 2003
Summary: New optimality conditions are derived for a class of shape optimization problems. The conditions are established on the boundary by an application of the boundary variations technique and in the interior of an optimal domain by exploiting the topological derivative method.
Jan Sokolowski, Antoni Zochowski
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On Second-Order Optimality Conditions for Vector Optimization

Journal of Optimization Theory and Applications, 2011
A vector optimization problem (VOP) is considered. The feasible set is stated by means of equality and inequality constraints. Two constraint qualifications has been borrowed from the scalar case and used for VOP. The first one (Kuhn-Tucker constraint qualification KTCQ) is based on a feasible arc and implies that the set of feasible and descent ...
María Cristina Maciel, Sandra A. Santos 0001, Graciela N. Sottosanto   +2 more
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Network optimality conditions Network optimality conditions

2023
Osmolovskii, Nikolai P, Meizhi Qian, Sokolowski, Jan   +2 more
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Optimality Conditions for Optimization Problems with Complementarity Constraints

SIAM Journal on Optimization, 1999
The motivation to study an optimization problem with complementarity constraints arose from a certain optimization problem with variational inequality constraints dealt with in a recent book by \textit{Z. Luo}, \textit{J. Pang}, and \textit{D. Ralph} [Mathematical programs with equilibrium constraints. Cambridge Univ. Press (1997; Zbl 0898.90006)]. The
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