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160
FPTAS for optimizing polynomials over the mixedinteger points of polytopes in fixed dimension
, 2006
"... We show the existence of a fully polynomialtime approximation scheme (FPTAS) for the problem of maximizing a nonnegative polynomial over mixedinteger sets in convex polytopes, when the number of variables is fixed. Moreover, using a weaker notion of approximation, we show the existence of a fully ..."
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Cited by 3 (2 self)
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We show the existence of a fully polynomialtime approximation scheme (FPTAS) for the problem of maximizing a nonnegative polynomial over mixedinteger sets in convex polytopes, when the number of variables is fixed. Moreover, using a weaker notion of approximation, we show the existence of a fully
Network formulations of mixedinteger programs
 In preparation
, 2006
"... We consider mixedinteger sets of the type MIX TU = {x: Ax ≥ b; xi integer, i ∈ I}, where A is a totally unimodular matrix, b is an arbitrary vector and I is a nonempty subset of the column indices of A. We show that the problem of checking nonemptiness of a set MIX TU is NPcomplete even in the cas ..."
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Cited by 11 (6 self)
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for the convex hull of MIX 2TU whose constraint matrix is a dual network matrix with an integral righthandside vector. The size of this formulation depends on the number of distinct fractional parts taken by the continuous variables in the extreme points of conv(MIX 2TU). When this number is polynomial
Note on the Complexity of the MixedInteger Hull of a Polyhedron
"... Abstract We study the complexity of computing the mixedinteger hull conv(P ∩ Z n × R d ) of a polyhedron P . Given an inequality description, with one integer variable, the mixedinteger hull can have exponentially many vertices and facets in d. For n, d fixed, we give an algorithm to find the mix ..."
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the mixed integer hull in polynomial time. Given P = conv(V ) and n fixed, we compute a vertex description of the mixedinteger hull in polynomial time and give bounds on the number of vertices of the mixed integer hull.
Efficient MixedInteger Planning for UAVs in Cluttered Environments
"... Abstract — We present a new approach to the design of smooth trajectories for quadrotor unmanned aerial vehicles (UAVs), which are free of collisions with obstacles along their entire length. To avoid the nonconvex constraints normally required for obstacleavoidance, we perform a mixedinteger opt ..."
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Cited by 1 (1 self)
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compute convex regions of safe space. This results in a substantially reduced number of integer variables, which improves the speed with which the optimization can be solved to its global optimum, even for tens or hundreds of obstacle faces. In addition, prior approaches have typically enforced obstacle
An Implicit Enumeration Algorithm for MixedInteger Linear Programming
"... An endeavour is made in this paper to present a novel implicit branch and bound method for mixed integer linear programming problems. The integer variables are driven to their nonbasic variables, which can be fixed, at either lower or upper bound, remaining nonbasic variables as such. The concept ..."
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An endeavour is made in this paper to present a novel implicit branch and bound method for mixed integer linear programming problems. The integer variables are driven to their nonbasic variables, which can be fixed, at either lower or upper bound, remaining nonbasic variables as such. The concept
An FPTAS for optimizing a class of lowrank functions over a polytope
, 2011
"... We present a fully polynomial time approximation scheme (FPTAS) for optimizing a very general class of nonlinear functions of low rank over a polytope. Our approximation scheme relies on constructing an approximate Paretooptimal front of the linear functions which constitute the given lowrank func ..."
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Cited by 7 (1 self)
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point of the polytope. Our technique can also be used to obtain an FPTAS for combinatorial optimization problems with nonlinear objective functions, for example when the objective is a product of a fixed number of linear functions. We also show that it is not possible to approximate the minimum of a
A PARAMETRIC INTEGER PROGRAMMING ALGORITHM FOR BILEVEL MIXED INTEGER PROGRAMS
, 2009
"... We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and mixed integer bilevel problems. For the mixed integer case wh ..."
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Cited by 2 (0 self)
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We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and mixed integer bilevel problems. For the mixed integer case
Integer polynomial optimization in fixed dimension
 MATHEMATICS OF OPERATIONS RESEARCH
, 2006
"... We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an integer polynomial over the lattice points of a convex polytope ..."
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Cited by 15 (7 self)
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We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an integer polynomial over the lattice points of a convex
Membrane system design for multicomponent gas mixtures via mixedinteger nonlinear programming
 Computer & Chemical Engineering
, 2000
"... An optimal design strategy for membrane networks separating multicomponent gas mixtures based on an approximate permeator model and mixedinteger nonlinear programming (MINLP) is proposed. A permeator system superstructure is used to embed a very large number of possible network configurations and a ..."
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Cited by 2 (0 self)
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An optimal design strategy for membrane networks separating multicomponent gas mixtures based on an approximate permeator model and mixedinteger nonlinear programming (MINLP) is proposed. A permeator system superstructure is used to embed a very large number of possible network configurations
Results 1  10
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160