We develop a method for generating valid convex quadratic inequalities for mixed 0-1 convex programs. We also show how these inequalities can be generated in the linear case by defining cut generation problems using a...
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We develop a method for generating valid convex quadratic inequalities for mixed 0-1 convex programs. We also show how these inequalities can be generated in the linear case by defining cut generation problems using a projection cone. The basic results for quadratic inequalities are extended to generate convex polynomial inequalities.
This paper considers planar location problems with rectilinear distance and barriers where the objective function is any convex, nondecreasing function of distance. Such problems have a non-convex feasible region and ...
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This paper considers planar location problems with rectilinear distance and barriers where the objective function is any convex, nondecreasing function of distance. Such problems have a non-convex feasible region and a nonconvex objective function. Based on an equivalent problem with modified barriers, derived in a companion paper [3], the non convex feasible set is partitioned into a network and rectangular cells. The rectangular cells are further partitioned into a polynomial number of convex subcells, called convex domains, on which the distance function, and hence the objective function, is convex. Then the problem is solved over the network and convex domains for an optimal solution. Bounds are given that reduce the number of convex domains to be examined. The number of convex domains is bounded above by a polynomial in the size of the problem.
In this paper we study the welldefinedness of the central path associated to a nonlinear convex semidefinite programming problem with smooth objective and constraint functions. Under standard assumptions, we prove tha...
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In this paper we study the welldefinedness of the central path associated to a nonlinear convex semidefinite programming problem with smooth objective and constraint functions. Under standard assumptions, we prove that the existence of the central path is equivalent to the nonemptiness and boundedness of the optimal set. Other equivalent conditions are given, such as the existence of a strictly dual feasible point or the existence of a single central point. The monotonic behavior of the primal and dual logarithmic barriers and of the primal and dual objective functions along the trajectory is also discussed. The existence and optimality of cluster points is established and finally, under the additional assumption of analyticity of the data functions, the convergence of the primal-dual trajectory is proved.
We present a formula for the optimal value f(c)(y) of the integer program max{c'x \ x is an element of Omega(y) boolean AND N-n} where Omega(y) is the convex polyhedron {x is an element of R-n \ Ax = y, x greater ...
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We present a formula for the optimal value f(c)(y) of the integer program max{c'x \ x is an element of Omega(y) boolean AND N-n} where Omega(y) is the convex polyhedron {x is an element of R-n \ Ax = y, x greater than or equal to 0}. It is a consequence of Brion and Vergne's formula which evaluates the sum Sigma(xis an element ofOmega(Y)boolean ANDNn)e(c') (x). As in linear programming, f(c)(y) can be obtained by inspection of the reduced-costs at the vertices of the polyhedron. We also provide an explicit result that relates f(c)(ty) and the optimal value of the associated continous linear program, for large values of t is an element of N.
We reduce the classification problem to solving a global optimization problem and a method based on a combination of the cutting angle method and a local search is applied to the solution of this problem. The proposed...
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We reduce the classification problem to solving a global optimization problem and a method based on a combination of the cutting angle method and a local search is applied to the solution of this problem. The proposed method allows to solve classification problems for databases with an arbitrary number of classes. Numerical experiments have been carried out with databases of small to medium size. We present their results and provide comparisons of these results with those obtained by 29 different classification algorithms. The best performance overall was achieved with the global optimization method.
This paper concerns an optimal control problem in single-stage manufacturing systems with finite output buffers. Given a sequence of jobs and their processing order, and given the release time and a due date for each ...
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ISBN:
(纸本)0780375165
This paper concerns an optimal control problem in single-stage manufacturing systems with finite output buffers. Given a sequence of jobs and their processing order, and given the release time and a due date for each job, the objective is to determine optimal processing times so as to minimize a cost functional consisting of lateness and earliness of the finished products. Jobs completed late are immediately delivered from the system, and jobs completed early are stored at an output buffer while waiting for their due dates. When the buffer gets full the server becomes blocked. Upper-bound and lower-bound constraints on the jobs' delivery times are imposed. The paper analyzes the problem and proposes an efficient algorithm for its. solution.
This paper shows how a class of objective functions can be incorporated into a prioritised, multi-objective optimisation problem, for which a solution can be obtained by solving a sequence of single-objective, constra...
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ISBN:
(纸本)078037388X
This paper shows how a class of objective functions can be incorporated into a prioritised, multi-objective optimisation problem, for which a solution can be obtained by solving a sequence of single-objective, constrained, convex programming problems. The objective functions considered in this paper typically arise in Model Predictive Control (MPC) of constrained, linear systems. The framework presented in this paper can be used to design a flexible, multi-objective MPC controller that takes priorities into account during the on-line computation of the control input.
This paper presents a two-stage robust model predictive control (RMPC) algorithm named as IRMPC for uncertain linear integrating plants described by a state-space model with input constraints. The global convergence o...
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This paper presents a two-stage robust model predictive control (RMPC) algorithm named as IRMPC for uncertain linear integrating plants described by a state-space model with input constraints. The global convergence of the resulted closed loop system is guaranteed under mild assumption. The simulation example shows its validity and better performance than conventional Min-Max RMPC strategies.
This paper presents a two-stage robust model predictive control (RMPC) algorithm named as IRMPC for uncertain linear integrating plants described by a state-space model with input constraints. The global convergence o...
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This paper presents a two-stage robust model predictive control (RMPC) algorithm named as IRMPC for uncertain linear integrating plants described by a state-space model with input constraints. The global convergence of the resulted closed loop system is guaranteed under mild assumption. The simulation example shows its validity and better performance than conventional Min-Max RMPC strategies.
Given a finite number of closed convex sets whose algebraic representation is known, we study the problem of finding the minimum of a convex function on the closure of the convex hull of the union of those sets. We de...
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Given a finite number of closed convex sets whose algebraic representation is known, we study the problem of finding the minimum of a convex function on the closure of the convex hull of the union of those sets. We derive an algebraic characterization of the feasible region in a higher-dimensional space and propose a solution procedure akin to the interior-point approach for convex programming.
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