This paper studies a bilevel programming problem with linear constraints, and in which the objective functions at both levels are concave bottleneck functions which are to be minimized. The problem is a non-convex pro...
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This paper studies a bilevel programming problem with linear constraints, and in which the objective functions at both levels are concave bottleneck functions which are to be minimized. The problem is a non-convex programming problem. It is shown that an optimal solution to the problem is attainable at an extreme point of the underlying region. The outer level objective function values are ranked in increasing order until a value is reached, one of the solutions corresponding to which is feasible for the problem. This solution is then the required global optimal solution.
To reduce the computational overhead in quantitative feedback theory (QFT) bound computation, only the (nonconvex) outside edge of a template should be used. This note presents an algorithm to calculate the nonconvex ...
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To reduce the computational overhead in quantitative feedback theory (QFT) bound computation, only the (nonconvex) outside edge of a template should be used. This note presents an algorithm to calculate the nonconvex hull with minimum concave radius defined by the feedback system specifications. [S0022-0434(00)01301-0].
The main purpose of this paper is the study of connections between combinatorial and continuous optimization. After reviewing some known results, new ways of establishing connections between the two fields are discuss...
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The main purpose of this paper is the study of connections between combinatorial and continuous optimization. After reviewing some known results, new ways of establishing connections between the two fields are discussed. Particularly, the importance of connecting combinatorial optimization with the field of variational inequalities is stressed. Related to this, the so-called gap function approach to solve a variational inequality is generalized, showing that methods for nonconvex and combinatorial programming may be useful in the variational field. Duality and further investigations are discussed.
The article focuses on the evolution of the Reformulation-Linearization/Convexification Technique (RLT). It notes that while RLT process leads to tight linear programming relaxations for the underlying discrete or con...
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The article focuses on the evolution of the Reformulation-Linearization/Convexification Technique (RLT). It notes that while RLT process leads to tight linear programming relaxations for the underlying discrete or continuous nonconvex problems being solved, one has to contend with the repeated solutions of such large-scale linear programs. It also mentions that as RLT and other related methods for continuous nonconvex programs have matured, an osmosis of different concepts from the domain of discrete optimization has occurred.
The evolution of the bilinear programming problem is reviewed and a new, more general model is discussed. The model involves two decision vectors and reduces to a linear program when one of the decision vectors is fix...
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The evolution of the bilinear programming problem is reviewed and a new, more general model is discussed. The model involves two decision vectors and reduces to a linear program when one of the decision vectors is fixed. The class of problems under consideration contains traditional bilinear programs, general quadratic programs, and bilinearly constrained and quadratically constrained extensions of these problems. We describe how several important applications from the literature, including the multiple modular design problem, can be modeled as generalized bilinear programs. Finally, we derive a linear programming relaxation that can be used as a subproblem in algorithmic solution schemes based on outer approximation and branch and bound.
This paper gives several sets of sufficient conditions that a local solution. x(k) exists of the problem min(Rk)f(k)(x), k = 1, 2, ..., such that {x(k)} has duster points that are local solutions of a problem of. the ...
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This paper gives several sets of sufficient conditions that a local solution. x(k) exists of the problem min(Rk)f(k)(x), k = 1, 2, ..., such that {x(k)} has duster points that are local solutions of a problem of. the form min(Rf)(x). The results are based on a well-known concept of topological, or point-wise convergence of the sets {R(k)} to R. Such results have been used to construct and validate large classes of mathematical programming methods based on successive approximations of the problem functions. They are also directly applicable to parametric and sensitivity analysis and provide additional characterizations of optimality for large classes of nonlinear programming problems.
A method is described for globally minimizing concave functions over convex sets whose defining constraints may be nonlinear. The algorithm generates linear programs whose solutions minimize the convex envelope of the...
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A method is described for globally minimizing concave functions over convex sets whose defining constraints may be nonlinear. The algorithm generates linear programs whose solutions minimize the convex envelope of the original function over successively tighter polytopes enclosing the feasible region. The algorithm does not involve cuts of the feasible region, requires only simplex pivot operations and univariate search computations to be performed, allows the objective function to be lower semicontinuous and nonseparable, and is guaranteed to converge to the global solution. Computational aspects of the algorithm are discussed.
As shown by D. Barnette (1973, J. Combin. Theory Ser. A 14, 37 53) there are precisely 39 simplicial 3-spheres with 8 vertices. Thirty-seven of these are boundary complexes for convex 4-polytopes. In this paper we sup...
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As shown by D. Barnette (1973, J. Combin. Theory Ser. A 14, 37 53) there are precisely 39 simplicial 3-spheres with 8 vertices. Thirty-seven of these are boundary complexes for convex 4-polytopes. In this paper we supply nonconvex embeddings in Euclidean 4-space for the remaining two 3-spheres, We discuss the properties of the embeddings as well as the techniques used to demonstrate their validity. (C) 2002 Elsevier Science (USA).
We deal with the nonconvex program called Generalized Lattice Point Problem. Here, a linear function is to be minimized over such points of a polyhedron which belong to the at most q-dimensional faces of another polyh...
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We deal with the nonconvex program called Generalized Lattice Point Problem. Here, a linear function is to be minimized over such points of a polyhedron which belong to the at most q-dimensional faces of another polyhedron. We present a finite cutting plane algorithm for solving the considered problem. Computational experience is also provided.
We investigate a variational approach to nonpotential perturbations of gradient flows of nonconvex energies in Hilbert spaces. We prove existence of solutions to elliptic-in-time regularizations of gradient flows by c...
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We investigate a variational approach to nonpotential perturbations of gradient flows of nonconvex energies in Hilbert spaces. We prove existence of solutions to elliptic-in-time regularizations of gradient flows by combining the minimization of a parameter-dependent functional over entire trajectories and a fixed-point argument. These regularized solutions converge up to subsequences to solutions of the gradient flow as the regularization parameter goes to zero. Applications of the abstract theory to nonlinear reaction diffusion systems are presented. (C) 2016 Elsevier Inc. All rights reserved.
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