This paper addresses the problem of reducing CO2 emissions by applying convex optimal power flow model to the combined economic and emission dispatch problem. The large amount of CO2 emissions in the power industry is a major source of global warming effect. An efficient and economic approach to reduce CO2 emissions is to formulate the emission reduction problem as emission dispatch problem and...

This thesis examines two problems concerning the secure and reliable operation of the electric power grid. The first part studies the distributed operation of the electric power grid using the power flow problem, which is vital to the operation of the grid. The power flow problem is a feasibility problem for finding an assignment of complex bus voltages that satisfies the power flow equations a...

We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation parameters in a specific self-adapting manner. This strategy that controls the relaxation parameters in a specific manner leaves enough user-flexibility but giv...

Simultaneous subgradient projection algorithms for the convex feasibility problem use subgradient calculations and converge sometimes even in the inconsistent case. We devise an algorithm that uses seminorm-induced oblique projections onto super half-spaces of the convex sets, which is advantageous when the subgradient-Jacobian is a sparse matrix at many iteration points of the algorithm. Using...

The projected subgradient method for constrained minimization repeatedly interlaces subgradient steps for the objective function with projections onto the feasible region, which is the intersection of closed and convex constraints sets, to regain feasibility. The latter poses a computational difficulty and, therefore, the projected subgradient method is applicable only when the feasible region ...

The Alternating Direction Method of Multipliers (ADMM) has received lots of attention recently due to the tremendous demand from large-scale and data-distributed machine learning applications. In this paper, we present a stochastic setting for optimization problems with non-smooth composite objective functions. To solve this problem, we propose a stochastic ADMM algorithm. Our algorithm applies...

In this paper, we present a new iterative scheme for finding a common element of the solution set F of the split feasibility problem and the fixed point set F(T) of a right Bregman strongly quasi-nonexpansive mapping T in p-uniformly convex Banach spaces which are also uniformly smooth. We prove strong convergence theorem of the sequences generated by our scheme under some appropriate condition...

Bürgisser, Cucker, and Lotz [arxiv:math.NA/0610270] proved a general theorem providing smoothed analysis estimates for conic condition numbers of problems of numerical analysis. Applications to linear and polynomial equation solving were given. We show that a suitable modification of the general theorem in that paper, adapted to a spherical convex setting, allows to analyze condition numbers of...