The aim of this paper is the development of an algorithm to find the critical points of a box-constrained multi-objective optimization problem. The proposed algorithm is an interior point method based on suitable dire...
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The aim of this paper is the development of an algorithm to find the critical points of a box-constrained multi-objective optimization problem. The proposed algorithm is an interior point method based on suitable directions that play the role of gradient-like directions for the vector objective function. The method does not rely on an "a priori" scalarization and is based on a dynamic system defined by a vector field of descent directions in the considered box. The key tool to define the mentioned vector field is the notion of vector pseudogradient. We prove that the limit points of the solutions of the system satisfy the Karush-Kuhn-Tucker (KKT) first order necessary condition for the box-constrained multi-objective optimization problem. These results allow us to develop an algorithm to solve box-constrained multi-objective optimization problems. Finally, we consider some test problems where we apply the proposed computational method. The numerical experience shows that the algorithm generates an approximation of the local optimal Pareto front representative of all parts of optimal front. (C) 2007 Elsevier B.V. All rights reserved.
In some applications, the comparison between two elements may depend on the point leading to the so called variable order structure. Optimality concepts may be extended to this more general framework. In this paper, w...
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In some applications, the comparison between two elements may depend on the point leading to the so called variable order structure. Optimality concepts may be extended to this more general framework. In this paper, we extend the steepest descent-likemethod for smooth unconstrained vector optimization problems under a variable order structure. Roughly speaking, we see that every accumulation point of the generated sequence satisfies a necessary first order condition. We discuss the consequence of this fact in the convex case.
In many non-convex optimization-based signal recovery tasks, a good initial point is essential for the performance of the optimization process. One seeks to start the point from a small local region surrounding the ta...
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In many non-convex optimization-based signal recovery tasks, a good initial point is essential for the performance of the optimization process. One seeks to start the point from a small local region surrounding the targeted signal. Then an efficient iterative refinement procedure can help recover the wanted signal. Motivated by this fact, we introduce two efficient and robust estimators to find reasonably good initial points for non-convex phase retrieval algorithms. The proposed estimators can provide high quality initial guesses for phase retrieval even with a number of samples that is close to the information-theoretic limit. The average relative error reduces exponentially as the oversampling ratio grows, which can improve the performance of existing non-convex optimization methods. The experimental results clearly demonstrate the superiority of two introduced estimators, which not only obtain a more accurate estimate of the true solution but also outperform the existing methods in terms of noise robustness when measurements are contaminated with noise.
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