We consider convex stochastic programming problems with probabilistic constraints involving integer-valued random variables. The concept of a p-efficient point of a probability distribution is used to derive various e...
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We consider convex stochastic programming problems with probabilistic constraints involving integer-valued random variables. The concept of a p-efficient point of a probability distribution is used to derive various equivalent problem formulations. Next we introduce the concept of r-concave discrete probability distributions and analyse its relevance for problems under consideration. These notions are used to derive lower and upper bounds for the optimal value of probabilistically constrained convex stochastic programming problems with discrete random variables.
The problem of determining a maximum matching or whether there exists a perfect matching, is very common in a large variety of applications and as been extensively studied in graph theory. In this paper we start to in...
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The problem of determining a maximum matching or whether there exists a perfect matching, is very common in a large variety of applications and as been extensively studied in graph theory. In this paper we start to introduce a characterisation of a family of graphs for which its stability number is determined by convex quadratic programming. The main results connected with the recognition of this family of graphs are also introduced. It follows a necessary and sufficient condition which characterise a graph with a perfect matching and an algorithmic strategy, based on the determination of the stability number of line graphs, by convex quadratic programming, applied to the determination of a perfect matching. A numerical example for the recognition of graphs with a perfect matching is described. Finally, the above algorithmic strategy is extended to the determination of a maximum matching of an arbitrary graph and some related results are presented.
In this paper we study robust convex quadratically constrained programs, a subset of the class of robust convex programs introduced by Ben-Tal and Nemirovski [4]. In contrast to [4], where it is shown that such robust...
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In this paper we study robust convex quadratically constrained programs, a subset of the class of robust convex programs introduced by Ben-Tal and Nemirovski [4]. In contrast to [4], where it is shown that such robust problems can be formulated as semidefinite programs, our focus in this paper is to identify uncertainty sets that allow this class of problems to be formulated as second-order cone programs (SOCP). We propose three classes of uncertainty sets for which the robust problem can be reformulated as an explicit SOCP and present examples where these classes of uncertainty sets are natural.
In this paper the generalized invex monotone functions are defined as an extension of monotone functions. A series of sufficient and necessary conditions are also given that relate the generalized invexity of the func...
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In this paper the generalized invex monotone functions are defined as an extension of monotone functions. A series of sufficient and necessary conditions are also given that relate the generalized invexity of the function theta with the generalized invex monotonicity of its gradient function deltheta. This new class of functions will be important in order to characterize the solutions of the Variational-like Inequality Problem and Mathematical programming Problem. (C) 2002 Elsevier Science B.V. All rights reserved.
This work relates to an actual loading problem at a bottleneck facility in a large refrigerator manufacturing plant. Items are loaded in specific combinations called phases which then move along different flow lines e...
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This work relates to an actual loading problem at a bottleneck facility in a large refrigerator manufacturing plant. Items are loaded in specific combinations called phases which then move along different flow lines encountering random rejections till assembly. To control shortages and inventory holdings periodically, a heuristic convex program is formulated with two forms of loss function: (a) piecewise linear and (b) quadratic. For all problem versions, the items' buffer state space admitted partitioning into polyhedral regions, with a particular form of loading policy being optimal in each region. The shapes of these regions depend on the loss function, leading to certain constraints on the parameters in the loss function. In a related paper (presented at the XXIX ORSE Convention, IIT-Bombay, Mumbai, December), numerous modifications to the policies derived here take into account the actual time-varying behaviour in several elements of the system. (C) 2003 Elsevier Science B.V. All rights reserved.
We introduce a novel optimization method based on semidefinite programming relaxations to the field of computer vision and apply it to the combinatorial problem of minimizing quadratic functionals in binary decision v...
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We introduce a novel optimization method based on semidefinite programming relaxations to the field of computer vision and apply it to the combinatorial problem of minimizing quadratic functionals in binary decision variables subject to linear constraints. The approach is (tuning) parameter-free and computes high-quality combinatorial solutions using interior-point methods (convex programming) and a randomized hyperplane technique. Apart from a symmetry condition, no assumptions (such as metric pairwise interactions) are made with respect to the objective criterion. As a consequence, the approach can be applied to a wide range of problems. Applications to unsupervised partitioning, figure-ground discrimination, and binary restoration are presented along with extensive ground-truth experiments. From the viewpoint of relaxation of the underlying combinatorial problem, we show the superiority of our approach to relaxations based on spectral graph theory and prove performance bounds.
This paper demonstrates that for generalized methods of multipliers for convex programming based on Bregman distance kernels - including the classical quadratic method of multipliers - the minimization of the augmente...
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This paper demonstrates that for generalized methods of multipliers for convex programming based on Bregman distance kernels - including the classical quadratic method of multipliers - the minimization of the augmented Lagrangian can be truncated using a simple, generally implementable stopping criterion based only on the norms of the primal iterate and the gradient (or a subgradient) of the augmented Lagrangian at that iterate. Previous results in this and related areas have required conditions that are much harder to verify, such as epsilon-optimality with respect to the augmented Lagrangian, or strong conditions on the convex program to be solved. Here, only existence of a KKT pair is required, and the convergence properties of the exact form of the method are preserved. The key new element in the analysis is the use of a full conjugate duality framework, as opposed to mainly examining the action of the method on the standard dual function of the convex program. An existence result for the iterates, stronger than those possible for the exact form of the algorithm, is also included.
The paper provides two contributions. First, we present new convergence results for conditional epsilon-subgradient algorithms for general convex programs. The results obtained here extend the classical ones by Polyak...
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The paper provides two contributions. First, we present new convergence results for conditional epsilon-subgradient algorithms for general convex programs. The results obtained here extend the classical ones by Polyak [Sov. Math. Doklady 8 (1967) 593;USSR Comput. Math. Math. Phys. 9 (1969) 14;Introduction to Optimization, Optimization Software, New York, 1987] as well as the recent ones in [Math. Program. 62 (1993) 261;Eur. J. Oper. Res. 88 (1996) 382;Math. Program. 81 (1998) 23] to a broader framework. Secondly, we establish the application of this technique to solve non-strictly convex-concave saddle point problems, such as primal-dual formulations of linear programs. Contrary to several previous solution algorithms for such problems, a saddle-point is generated by a very simple scheme in which one component is constructed by means of a conditional epsilon-subgradient algorithm, while the other is constructed by means of a weighted average of the (inexact) subproblem solutions generated within the subgradient method. The convergence result extends those of [Minimization Methods for Non-Differentiable Functions, Springer-Verlag, Berlin, 1985;Oper. Res. Lett. 19 (1996) 105;Math. Program. 86 (1999) 283] for Lagrangian saddle-point problems in linear and convex programming, and of [Int. J. Numer. Meth. Eng. 40 (1997) 1295] for a linear-quadratic saddle-point problem arising in topology optimization in contact mechanics. (C) 2002 Elsevier B.V. All rights reserved.
This note treats the problem of stabilization of linear systems by static output feedback using the concept of (C, A, B)-invariant subspaces. The work provides a new characterization of output stabitizable (C, A, B)-i...
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This note treats the problem of stabilization of linear systems by static output feedback using the concept of (C, A, B)-invariant subspaces. The work provides a new characterization of output stabitizable (C, A, B)-invariant subspaces through two coupled quadratic stabilization conditions. An equivalence is shown between the existence of a solution to this set of conditions and the possibility to stabilize the system by, static output feedback. An algorithm is provided and numerical examples are reported to illustrate the approach.
In this paper we study the (Berge) upper semicontinuity of a generic multifunction assigning to each parameter, in a metric space, a closed convex subset of the n-dimensional Euclidean space. A relevant particular cas...
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In this paper we study the (Berge) upper semicontinuity of a generic multifunction assigning to each parameter, in a metric space, a closed convex subset of the n-dimensional Euclidean space. A relevant particular case arises when we consider the feasible set mapping associated with a parametric family of convex semi-infinite programming problems. Related to such a generic multifunction, we introduce the concept of epsilon-reinforced mapping, which will allow us to establish a sufficient condition for the aimed property. This condition turns out to be also necessary in the case that the boundary of the image set at the nominal value of the parameter contains no half-lines. On the other hand, it is well-known that every closed convex set in the Euclidean space can be viewed as the solution set of a linear semi-infinite inequality system and, so, a parametric family of linear semi-infinite inequality systems can always be associated with the original multifunction. In this case, a different necessary condition is provided in terms of the coefficients of these linear systems. This condition tries to measure the relative variation of the right hand side with respect to the left hand side of the constraints of the systems in a neighbourhood of the nominal parameter.
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