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作者：Abada, Ibrahim; d'Aertrycke, Gauthier de Maere; Smeers, Yves
作者单位：Engie; Engie; Universite Catholique Louvain
摘要：Investment in generation capacity has traditionally been evaluated by computing the present value of cashflows accruing from new equipment in a market with globally optimized capacity mix. The competition and risk that now prevail in the sector may require a more refined analysis. We consider a competitive market with agents investing in some mix of capacities: the risk exposure of a plant and the attitude towards risk of the owner depend on the plant and the portfolio of its capacities. They ...
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作者：Birgin, E. G.; Gardenghi, J. L.; Martinez, J. M.; Santos, S. A.; Toint, Ph. L.
作者单位：Universidade de Sao Paulo; Universidade Estadual de Campinas; University of Namur; University of Namur
摘要：The worst-case evaluation complexity for smooth (possibly nonconvex) unconstrained optimization is considered. It is shown that, if one is willing to use derivatives of the objective function up to order p (for p >= 1) and to assume Lipschitz continuity of the p-th derivative, then an epsilon-approximate first-order critical point can be computed in at most O(epsilon -((p+1)/p)) evaluations of the problem's objective function and its derivatives. This generalizes and subsumes results known for...
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作者：Zhou, Zirui; So, Anthony Man-Cho
作者单位：Chinese University of Hong Kong
摘要：Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for solving optimization problems. In this paper, we present a new framework for establishing error bounds for a class of structured convex optimization problems, in which the objective function is the sum of a smooth convex function and a general closed proper conve...
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作者：Consolini, Luca; Locatelli, Marco
作者单位：University of Parma
摘要：The complexity of quadratic programming problems with two quadratic constraints is an open problem. In this paper we show that when one constraint is a ball constraint and the Hessian of the quadratic function defining the other constraint is positive definite, then, under quite general conditions, the problem can be solved in polynomial time in the real-number model of computation through an approach based on the analysis of the dual space of the Lagrange multipliers. However, the degree of t...
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作者：Schmidt, Mark; Le Roux, Nicolas; Bach, Francis
作者单位：University of British Columbia
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作者：Firsching, Moritz
作者单位：Free University of Berlin
摘要：We show that nonlinear optimization techniques can successfully be applied to realize and to inscribe matroid polytopes and simplicial spheres. In order to show non-realizability of simplicial spheres, we extend the method of finding biquadratic final polynomials for matroid polytopes to partial matroid polytopes. Combining these two methods we obtain a complete classification of neighborly polytopes of dimension 4, 6 and 7 with 11 vertices, of neighborly 5-polytopes with 10 vertices, as well ...
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作者：Timoshin, Sergey A.
作者单位：Irkutsk Science Centre of the Russian Academy of Sciences; Russian Academy of Sciences; Matrosov Institute for System Dynamics & Control Theory SB RAS
摘要：We consider a differential inclusion of subdifferential type with a nonconvex and unbounded valued perturbation. Existence and relaxation results are obtained for this inclusion. By relaxation we mean approximation of a solution of the differential inclusion with convexified perturbation by solutions of the given inclusion. The traditional condition of Lipschitz continuity for such kind of problems is weakened and a somehow more appropriate in the context of unbounded valued multifunctions tru...
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作者：Lamm, Michael; Lu, Shu; Budhiraja, Amarjit
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine
摘要：Stochastic variational inequalities (SVIs) provide a means for modeling various optimization and equilibrium problems where data are subject to uncertainty. Often the SVI cannot be solved directly and requires a numerical approximation. This paper considers the use of a sample average approximation and proposes three methods for computing confidence intervals for components of the true solution. The first two methods use an indirect approach that requires initially computing asymptotically exa...
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作者：Rockafellar, R. Tyrrell; Wets, Roger J-B
作者单位：University of Washington; University of Washington Seattle; University of California System; University of California Davis
摘要：Variational inequality modeling, analysis and computations are important for many applications, but much of the subject has been developed in a deterministic setting with no uncertainty in a problem's data. In recent years research has proceeded on a track to incorporate stochasticity in one way or another. However, the main focus has been on rather limited ideas of what a stochastic variational inequality might be. Because variational inequalities are especially tuned to capturing conditions ...
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作者：Queyranne, Maurice; Wolsey, Laurence A.
作者单位：Universite Catholique Louvain; University of British Columbia
摘要：Switching machines on and off is an important aspect of unit commitment problems and production planning problems, among others. Here we study tight mixed integer programming formulations for two aspects of such problems: bounded length on- and off-intervals, and interval-dependent start-ups. The problem with both these aspects admits a general Dynamic Programming (shortest path) formulation which leads to a tight extended formulation with a number of binary variables that is quadratic in the ...
