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In this paper we propose new methods for solving huge-scale optimization problems. For problems of this size, even the simplest full-dimensional vector operations are very expensive. Hence, we propose to apply an optimization technique based on random partial update of decision variables. For...
Persistent link: https://www.econbiz.de/10008550209
Problems dealing with the design and the operations of gas transmission networks are challenging. The difficulty mainly arises from the simultaneous modeling of gas transmission laws and of the investment costs. The combination of the two yields a non- linear non-convex optimization problem. To...
Persistent link: https://www.econbiz.de/10008550235
In this paper, we prove the complexity bounds for methods of Convex Optimization based only on computation of the function value. The search directions of our schemes are normally distributed random Gaussian vectors. It appears that such methods usually need at most n times more iterations than...
Persistent link: https://www.econbiz.de/10009002079
In this paper, we analyze different first-order methods of smooth convex optimization employing inexact first-order information. We introduce the notion of an approximate first-order oracle. The list of examples of such an oracle includes smoothing technique, Moreau-Yosida regularization,...
Persistent link: https://www.econbiz.de/10009002083
In this paper, we solve a class of convex infinite-dimensional optimization problems using a numerical approximation method that does not rely on discretization. Instead, we restrict the decision variable to a sequence of finite-dimensional linear subspaces of the original infinite-dimensional...
Persistent link: https://www.econbiz.de/10008642212
In this paper, we propose an efficient technique for solving some infinite-dimensional problems over the sets of functions of time. In our problem, besides the convex point-wise constraints on state variables, we have convex coupling constraints with finite-dimensional image. Hence, we can...
Persistent link: https://www.econbiz.de/10008642227
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