Journal of Global Optimization
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Augmented Lagrangian Duality and Nondifferentiable Optimization Methods in Nonconvex Programming
Journal of Global Optimization - - 2002
In this paper we present augmented Lagrangians for nonconvex minimization problems with equality constraints. We construct a dual problem with respect to the presented here Lagrangian, give the saddle point optimality conditions and obtain strong duality results. We use these results and modify the subgradient and cutting plane methods for solving the dual problem constructed. Algorithms proposed ......
A bisection-extreme point search algorithm for optimizing over the efficient set in the linear dependence case
Journal of Global Optimization - Tập 3 - Trang 95-111 - 1993
The algorithms and algorithmic ideas currently available for globally optimizing linear functions over the efficient sets of multiple objective linear programs either use nonstandard subroutines or cannot yet be implemented for lack of sufficient development. In this paper a Bisection-Extreme Point Search Algorithm is presented for globally solving a large class of such problems. The algorithm fin......
ORCA: Outlier detection and Robust Clustering for Attributed graphs
Journal of Global Optimization - Tập 81 Số 4 - Trang 967-989 - 2021
Optimal deterministic algorithm generation
Journal of Global Optimization - Tập 71 - Trang 891-913 - 2018
A formulation for the automated generation of algorithms via mathematical programming (optimization) is proposed. The formulation is based on the concept of optimizing within a parameterized family of algorithms, or equivalently a family of functions describing the algorithmic steps. The optimization variables are the parameters—within this family of algorithms—that encode algorithm design: the co......
Ab initio Tertiary Structure Prediction of Proteins
Journal of Global Optimization - Tập 25 - Trang 113-140 - 2003
A daunting challenge in the area of computational biology has been to develop a method to theoretically predict the correct three-dimensional structure of a protein given its linear amino acid sequence. The ability to surmount this challenge, which is known as the protein folding problem, has tremendous implications. We introduce a novel ab initio approach for the protein folding problem. The accu......
An application of Lipschitzian global optimization to product design
Journal of Global Optimization - Tập 1 - Trang 389-401 - 1991
The issue of finding feasible mixture designs is formulated and solved as a Lipschitzian global optimization problem. The solution algorithm is based on a simplicial partition strategy. Implementation aspects and extension possibilities are treated in some detail, providing also numerical examples.
A globally convergent method for semi-infinite linear programming
Journal of Global Optimization - Tập 8 - Trang 189-199 - 1996
This paper presents a globally convergent method for solving a general semi-infinite linear programming problem. Some important features of this method include: It can solve a semi-infinite linear program having an unbounded feasible region. It requires an inexact solution to a nonlinear subproblem at each iteration. It allows unbounded index sets and nondifferentiable constraints. The amount of w......
Stackelberg equilibria via variational inequalities and projections
Journal of Global Optimization - Tập 57 - Trang 821-828 - 2012
Existence and location of Stackelberg equilibria is studied for two players by using appropriate variational inequalities and fixed point arguments. Both compact and non-compact strategy sets are considered in Euclidean spaces; in the non-compact case, we apply arguments from the theory of (discrete and continuous) projective dynamical systems. Some examples are also presented.
Duality on a nondifferentiable minimax fractional programming
Journal of Global Optimization - Tập 54 - Trang 295-306 - 2010
We establish the necessary and sufficient optimality conditions on a nondifferentiable minimax fractional programming problem. Subsequently, applying the optimality conditions, we constitute two dual models: Mond-Weir type and Wolfe type. On these duality types, we prove three duality theorems—weak duality theorem, strong duality theorem, and strict converse duality theorem.
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