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We consider a projected gradient method equipped with the nonmonotone line search procedure for convex constrained multiobjective optimization problems. Under mild assumptions, we show the convergence of the full sequence generated by the algorithm to a weak Pareto optimal point. Furthermore, under some appropriate Lipschitz continuity assumption of the gradients of objective functions, a linear convergence result for this method is also established. [ABSTRACT FROM AUTHOR]

In order to ensure the path continuity of redundant manipulators with constrained motion planning, this paper proposed a rapidly exploring random trees algorithm with progressive constraint extension ( PCE-RRT) for the constrained failure and path failure problems of direct interpolation and continuous interpolation. The algorithm introduced a progressive constrained extension method when performing tree expansion, which used the inverse kinematics method with the nearest point information, iteratively shortened the distance between the nearest point and the extended point while ensuring the task constraint, so that each extension could guarantee the constraint and continuity of the tree. PCE-RRT could make the final tree fit well into the constrained manifold subspace, and any two connected nodes in the search tree could satisfy the continuous condition. The simulation experiments verify the validity of the algorithm, and the results show that the proposed algorithm can provide a path solution that satisfied the constraints and continuity conditions for the manipulator constrained motion planning problem. [ABSTRACT FROM AUTHOR]

Abstract: The object of this paper is to perform an analysis of the sensitivity for convex vector programs with inequality constraints by examining the quantitative behavior of a certain set of optima according to changes of right-hand side parameters included in the program. The results in the paper prove that the sensitivity of the program depends on the solution of a dual program and its sensitivity. [Copyright &y& Elsevier]

In order to find sparse approximations of signals, an appropriate generative model for the signal class has to be known. If the model is unknown, it can be adapted using a set of training samples. This paper presents a novel method for dictionary learning and extends the learning problem by introducing different constraints on the dictionary. The convergence of the proposed method to a fixed point is guaranteed, unless the accumulation points form a continuum. This holds for different sparsity measures. The majorization method is an optimization method that substitutes the original objective function with a surrogate function that is updated in each optimization step. This method has been used successfully in sparse approximation and statistical estimation [e.g., expectation-maximization (EM)] problems. This paper shows that the majorization method can be used for the dictionary learning problem too. The proposed method is compared with other methods on both synthetic and real data and different constraints on the dictionary are compared. Simulations show the advantages of the proposed method over other currently available dictionary learning methods not only in terms of average performance but also in terms of computation time. [ABSTRACT FROM AUTHOR]