Journal ArticleDOI
Unboundedness of a convex quadratic function subject to concave and convex quadratic constraints
TLDR
In this paper, conditions for the existence of upper and lower bounds on convex quadratic objective functions subject to concave and convex Quadratic Constraint Constraints are presented.About:
This article is published in European Journal of Operational Research.The article was published on 1992-11-25. It has received 13 citations till now. The article focuses on the topics: Convex analysis & Concave function.read more
Citations
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Journal ArticleDOI
Second-order global optimality conditions for convex composite optimization
TL;DR: Second-order optimality conditions are obtained of aglobal minimizer for convex composite problems with a non-finite valued convex function and a twice strictly differentiable function by introducing a generalized representation condition.
Journal ArticleDOI
On Generalizations of the Frank-Wolfe Theorem to Convex and Quasi-Convex Programmes
TL;DR: It is proved that the optimal solution set of the considered problem is nonempty, this way extending the attainability result well known as the so-called Frank-Wolfe theorem.
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An algorithm to determine boundedness of quadratically constrained convex quadratic programmes
TL;DR: In this paper, the authors present an algorithm which can be used to determine whether or not a convex quadratic objective function is bounded from below over a feasible region defined by convex Quadratic constraints.
Journal ArticleDOI
Convex constrained programmes with unattained infima
TL;DR: In this paper, the authors derived the equation of the feasible parametrized curve C ( t ) such that the infimum of the logarithmic penalty function along this curve is equal to the global infimum over the region R.
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Conditions for boundedness in concave programming under reverse convex and convex constraints
TL;DR: This paper presents necessary and sufficient conditions for boundedness of a feasible region defined by reverse convex constraints and establishes sufficient and necessary conditions for existence of an upper bound for a convex objective function defined over the system of concave inequality constraints.
References
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Book
Nonlinear Programming
TL;DR: It is shown that if A is closed for all k → x x, k → y y, where ( k A ∈ ) k y x , then ( ) A ∉ y x .
Journal ArticleDOI
LINPACK User's Guide.
TL;DR: The use of least-squares techniques for this and G. W. Stewart, LINPACK Users' Guide for Intel® Math Kernel Library 11.3 for Linux* OS are provided.
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Quadratically constrained quadratic programming: Some applications and a method for solution
TL;DR: A constructive method is used to prove that ∩Ci is not empty and thatx (û) withi∈M û ∈∩ Ci characterizes an optimal solution to (QPQR).
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A method of analytic centers for quadratically constrained convex quadratic programs
Sanjay Mehrotra,Jie Sun +1 more
TL;DR: In this paper, an interior point method is developed for maximizing a concave quadratic function under convex quadrastic constraints, which constructs a sequence of nested convex sets and finds their approximate centers using a partial Newton step.
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Quadratic programming with quadratic constraints
TL;DR: In this article, two duals of a program with a quadratic objective function and constraints are provided, and an algorithm is presented based upon approximations to the duals.