The convergence of the algorithm for solving convex feasibility problem is studied by the method of sequential averaged and relaxed projections. Some results of H. H. Bauschke and J. M. Borwein are generalized by introducing new methods. Examples illustrating these generalizations are given.

A computationally-efficient method for recovering sparse signals from a series of noisy observations, known as the problem of compressed sensing (CS), is presented. The theory of CS usually leads to a constrained convex minimization problem. In this work, an alternative outlook is proposed. Instead of solving the CS problem as an optimization problem, it is suggested to transform the optimizati...

We study finite convergence of the modified cyclic subgradient projections (MCSP) algorithm for the convex feasibility problem (CFP) in the Euclidian space. Expanding control sequences allow the indices of the sets of the CFP to re-appear and be used again by the algorithm ∗Currently with the Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, Ma...

The analysis of flow in water-distribution networks with several pumps by the Content Model may be turned into a non-convex optimization uncertain problem with multiple solutions. Newton-based methods such as GGA are not able to capture a global optimum in these situations. On the other hand, evolutionary methods designed to use the population of individuals may find a global solution even for ...

Economic dispatch with valve point effect and Prohibited Operating Zones (POZs) is a non-convex and discontinuous optimization problem. Harmony Search (HS) is one of the recently presented meta-heuristic algorithms for solving optimization problems, which has different variants. The performances of these variants are severely affected by selection of different parameters of the algorithm. Intel...

We describe an infeasible interior point algorithm for convex minimization problems. The method uses quasi-Newton techniques for approximating the second derivatives and providing superlinear convergence. We propose a new feasibility control of the iterates by introducing shift variables and by penalizing them in the barrier problem. We prove global convergence under standard conditions on the ...

the problem of finding the minimum cost multi-commodity flow in an undirected and completenetwork is studied when the link costs are piecewise linear and convex. the arc-path model and overflowmodel are presented to formulate the problem. the results suggest that the new overflow model outperformsthe classical arc-path model for this problem. the classical revised simplex, frank and wolf and a ...

In this chapter a randomized ellipsoid algorithm is described that can be used for finding solutions to robust Linear Matrix Inequality (LMI) problems. The iterative algorithm enjoys the property that the convergence speed is independent on the number of uncertain parameters. Other advantages, as compared to the deterministic algorithms, are that the uncertain parameters can enter the LMIs in a...

In this paper a new method is introduced for path planning of an autonomous vehicle. In this method, the environment is considered cluttered and with some uncertainty sources. Thus, the state of detected object should be estimated using an optimal filter. To do so, the state distribution is assumed Gaussian. Thus the state vector is estimated by a Kalman filter at each time step. The estimation...

We propose an approximation algorithm based on the Lagrangian or price directive decomposition method to compute an -approximate solution of the mixed fractional packing and covering problem: find x 2 B such that f(x) (1 + )a, g(x) (1 )b where f(x); g(x) are vectors with M nonnegative convex and concave functions, a and b are M dimensional nonnegative vectors and B is a convex set that can be q...