Active set and interior methods for nonlinear optimization.
Byrd, Richard H., Nocedal, Jorge (1998)
Documenta Mathematica
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Displaying similar documents to “Nonsmooth equation method for nonlinear nonconvex optimization”
Active set and interior methods for nonlinear optimization.
A comparative study on optimization methods for the constrained nonlinear programming problems.
Yeniay, Ozgur (2005)
Mathematical Problems in Engineering
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A second order -approximation method for constrained optimization problems involving second order invex functions
Tadeusz Antczak (2009)
Applications of Mathematics
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A new approach for obtaining the second order sufficient conditions for nonlinear mathematical programming problems which makes use of second order derivative is presented. In the so-called second order -approximation method, an optimization problem associated with the original nonlinear programming problem is constructed that involves a second order -approximation of both the objective function and the constraint function constituting the original problem. The equivalence between...
Integer Programming Formulation of the Bilevel Knapsack Problem
R. Mansi, S. Hanafi, L. Brotcorne (2010)
Mathematical Modelling of Natural Phenomena
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The Bilevel Knapsack Problem (BKP) is a hierarchical optimization problem in which the feasible set is determined by the set of optimal solutions of parametric Knapsack Problem. In this paper, we propose two stages exact method for solving the BKP. In the first stage, a dynamic programming algorithm is used to compute the set of reactions of the follower. The second stage consists in solving an integer program reformulation of BKP. We show that ...
Reduction of dimensionality in dynamic programming-based solution methods for nonlinear integer programming.
Ram, Balasubramanian, Babu, A.J.G. (1988)
International Journal of Mathematics and Mathematical Sciences
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Large-scale nonlinear programming algorithm using projection methods
Paweł Białoń (2000)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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A method for solving large convex optimization problems is presented. Such problems usually contain a big linear part and only a small or medium nonlinear part. The parts are tackled using two specialized (and thus efficient) external solvers: purely nonlinear and large-scale linear with a quadratic goal function. The decomposition uses an alteration of projection methods. The construction of the method is based on the zigzagging phenomenon and yields a non-asymptotic convergence, not...
Nonlinear multiple hybrid procedures for solving some constrained nonlinear optimization problems
B. Rhanizar (2002)
Applicationes Mathematicae
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We introduce a new formulation of multiple hybrid procedures which consist in a combination of k arbitrary approximate solutions. The connection between this method and other vector sequence transformations is studied. This connection is also exploited for solving some constrained nonlinear optimization problems. A convergence acceleration result is established and numerical examples are given.
A duality theorem for complex nonlinear programming
C. Das, J. Parida (1977)
Matematički Vesnik
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An Algorithm For Solving Multiple Objective Integer Linear Programming Problem
Moncef Abbas, Djamal Chaabane (2010)
RAIRO - Operations Research
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In the present paper a complete procedure for solving Multiple Objective Integer Linear Programming Problems is presented. The algorithm can be regarded as a corrected form and an alternative to the method that was proposed by Gupta and Malhotra. A numerical illustration is given to show that this latter can miss some efficient solutions. Whereas, the algorithm stated bellow determines all efficient solutions without missing any one.