The simplex algorithm travels, on the underlying polyhedron, from vertex to vertex until reaching an optimal vertex. With the same simplex framework, the proposed algorithm generates a series of feasible points (which are not necessarily vertices). In particular, it is exactly an interior point algorithm if the initial point used is interior. Computational experiments show … Read more
We present an on-line management strategy for photovoltaic-hydrogen (PV-H2) hybrid energy systems. The strategy follows a receding-horizon principle and exploits solar radiation forecasts and statistics generated through a Gaussian process model. We demonstrate that incorporating forecast information can dramatically improve the reliability and economic performance of these promising energy production devices. ArticleDownload View PDF
We consider the problems of finding a maximum clique in a graph and finding a maximum-edge biclique in a bipartite graph. Both problems are NP-hard. We write both problems as matrix-rank minimization and then relax them using the nuclear norm. This technique, which may be regarded as a generalization of compressive sensing, has recently been … Read more
We consider linear optimization over a fixed compact convex feasible region that is semi-algebraic (or, more generally, “tame”). Generically, we prove that the optimal solution is unique and lies on a unique manifold, around which the feasible region is “partly smooth”, ensuring finite identification of the manifold by many optimization algorithms. Furthermore, second-order optimality conditions … Read more
A simple unified framework is presented for the study of strong efficient solutions, weak efficient solutions, positive proper efficient solutions, Henig global proper efficient solutions, Henig proper efficient solutions, super efficient solutions, Benson proper efficient solutions, Hartley proper efficient solutions, Hurwicz proper efficient solutions and Borwein proper efficient solutions of set-valued optimization problem with/or without … Read more
Identification of active constraints in constrained optimization is of interest from both practical and theoretical viewpoints, as it holds the promise of reducing an inequality-constrained problem to an equality-constrained problem, in a neighborhood of a solution. We study this issue in the more general setting of composite nonsmooth minimization, in which the objective is a … Read more
An Asset-Liability Management model with a novel strategy for controlling risk of underfunding is presented in this paper. The basic model involves multiperiod decisions (portfolio rebalancing) and deals with the usual uncertainty of investment returns and future liabilities. Therefore it is well-suited to a stochastic programming approach. A stochastic dominance concept is applied to measure … Read more
Iterative processes based on Fejer mappings with diminishing problem-specific shifts in the arguments are considered. Such structure allows fine-tuning of Fejer processes by directing them toward selected subsets of attracting sets. Use of various Fejer operators provides ample opportunities for decomposition and parallel computations. Subgradient projection algorithms with sequential and simultaneous projections on segmented constraints … Read more
Robust portfolio optimization finds the worst-case portfolio return given that the asset returns are realized within a prescribed uncertainty set. If the uncertainty set is not too large, the resulting portfolio performs well under normal market conditions. However, its performance may substantially degrade in the presence of market crashes, that is, if the asset returns … Read more
We study the best OSPF style routing problem in telecommunication networks, where weight management is employed to get a routing configuration with the minimum oblivious ratio. We consider polyhedral demand uncertainty: the set of traffic matrices is a polyhedron defined by a set of linear constraints, and the performance of each routing is assessed on … Read more