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作者：Preda, D; Noailles, J
作者单位：Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National Polytechnique de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：Integrating logical constraints into optimal control problems is not an easy task. In fact, optimal control problems are usually continuous while logical constraints are naturally expressed by integer (binary) variables. In this article we are interested is a particular form of an LQR optimal control problem: the energy (control L-2 norm) is to be minimized, system dynamic is linear and logical constraints on the control use are to be fulfilled. Even if the starting continuous problem is not a...
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作者：Pritchard, G; Philpott, AB; Neame, PJ
作者单位：University of Auckland; University of Auckland; University of Technology Sydney
摘要：For a price-taking generator operating a hydro-electric reservoir in a pool electricity market, the optimal stack to offer in each trading period over a planning horizon can be computed using dynamic programming. However, the market trading period (usually 1 hour or less) may be much shorter than the inherent time scale of the reservoir (often many months). We devise a dynamic programming model for such situations in which each stage represents many trading periods. In this model, the decision...
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作者：Zheng, XY; Ng, KF
作者单位：Yunnan University; Chinese University of Hong Kong
摘要：Using variational analysis, we study vector optimization problems with objectives being closed multifunctions on Banach spaces or in Asplund spaces. In particular, in terms of the coderivatives, we present Fermat's rules as necessary conditions for an optimal solution of the above problems. As applications, we also provide some necessary conditions (in terms of Clarke's normal cones or the limiting normal cones) for Pareto efficient points.
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作者：Bhattacharjee, B; Lemonidis, P; Green, WH Jr; Barton, PI
作者单位：Massachusetts Institute of Technology (MIT)
摘要：Optimization problems involving a finite number of decision variables and an infinite number of constraints are referred to as semi-infinite programs (SIPs). Existing numerical methods for solving nonlinear SIPs make strong assumptions on the properties of the feasible set, e.g., convexity and/or regularity, or solve a discretized approximation which only guarantees a lower bound to the true solution value of the SIP. Here, a general, deterministic algorithm for solving semi-infinite programs ...
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作者：Gilbert, JC; Gonzaga, CC; Karas, E
作者单位：Universidade Federal de Santa Catarina (UFSC); Universidade Federal do Parana
摘要：This paper presents some examples of ill-behaved central paths in convex optimization. Some contain infinitely many fixed length central segments; others manifest oscillations with infinite variation. These central paths can be encountered even for infinitely differentiable data.
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作者：Stork, F; Uetz, M
作者单位：Maastricht University; Technical University of Berlin
摘要：We present several complexity results related to generation and counting of all circuits of an independence system. Our motivation to study these problems is their relevance in the solution of resource constrained scheduling problems, where an independence system arises as the subsets of jobs that may be scheduled simultaneously. We are interested in the circuits of this system, the so-called minimal forbidden sets, which are minimal subsets of jobs that must not be scheduled simultaneously. A...
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作者：Zhao, GY
作者单位：National University of Singapore
摘要：This paper presents an algorithm for solving multi-stage stochastic convex nonlinear programs. The algorithm is based on the Lagrangian dual method which relaxes the nonanticipativity constraints, and the barrier function method which enhances the smoothness of the dual objective function so that the Newton search directions can be used. The algorithm is shown to be of global convergence and of polynomial-time complexity.
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作者：Goldfarb, D; Scheinberg, K
作者单位：Columbia University; International Business Machines (IBM); IBM USA
摘要：Second-order cone programming (SOCP) problems are typically solved by interior point methods. As in linear programming (LP), interior point methods can, in theory, solve SOCPs in polynomial time and can, in practice, exploit sparsity in the problem data. Specifically, when cones of large dimension are present, the density that results in the normal equations that are solved at each iteration can be remedied in a manner similar to the treatment of dense columns in an LP. Here we propose a produ...
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作者：Lin, JG
摘要：This paper examines Pareto optimality of solutions to multi-objective problems scalarized in the min-norm, compromise programming, generalized goal programming, or unrestricted min-max formulations. Issues addressed include, among others, uniqueness in solution or objective space, penalization for overachievement of goals, min-max reformulation of goal programming, inferiority in Tchebycheff-nonn minimization, strength and weakness of weighted-bound optimization, quasi-satisficing decision-mak...
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作者：Meurdesoif, P
作者单位：Universite de Bordeaux
摘要：The Lovasz theta-number is a way to approximate the independence number of a graph, but also its chromatic number. We express the Lovasz bound as the continuous relaxation of a discrete Lovdsz theta-number which we derive from Karger et al.'s formulation, and which is equal to the chromatic number. We also give another relaxation a la Schrijver-McEliece, which is better than the Lovasz theta-number.
