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89
Universal Duality in Conic Convex Optimization
, 2005
"... Given a primaldual pair of linear programs, it is well known that if their optimal values are viewed as lying on the extended real line, then the duality gap is zero, unless both problems are infeasible, in which case the optimal values are + ∞ and −∞. In contrast, for optimization problems over no ..."
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nonpolyhedral convex cones, a nonzero duality gap can exist when either the primal or the dual is feasible. For a pair of dual conic convex programs, we provide simple conditions on the “constraint matrices ” and cone under which the duality gap is zero for every choice of linear objective function
Deriving Duality for l_pnorm Optimization Using Conic Optimization
, 1999
"... In this paper, we formulate the l p norm optimization problem as a conic optimization problem and derive its standard duality properties. We first define an ad hoc closed convex cone L and derive its dual. We express then the standard l p norm optimization primal problem as a conic problem involvi ..."
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In this paper, we formulate the l p norm optimization problem as a conic optimization problem and derive its standard duality properties. We first define an ad hoc closed convex cone L and derive its dual. We express then the standard l p norm optimization primal problem as a conic problem
Advances in convex optimization: Conic programming
 In Proceedings of International Congress of Mathematicians
, 2007
"... Abstract. During the last two decades, major developments in convex optimization were focusing on conic programming, primarily, on linear, conic quadratic and semidefinite optimization. Conic programming allows to reveal rich structure which usually is possessed by a convex program and to exploit ..."
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Cited by 23 (0 self)
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this structure in order to process the program efficiently. In the paper, we overview the major components of the resulting theory (conic duality and primaldual interior point polynomial time algorithms), outline the extremely rich “expressive abilities ” of conic quadratic and semidefinite programming
Linear precoding via conic optimization for fixed mimo receivers
 IEEE Trans. on Signal Processing
, 2006
"... We consider the problem of designing linear precoders for fixed multiple input multiple output (MIMO) receivers. Two different design criteria are considered. In the first, we minimize the transmitted power subject to signal to interference plus noise ratio (SINR) constraints. In the second, we maxi ..."
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Cited by 154 (3 self)
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maximize the worst case SINR subject to a power constraint. We show that both problems can be solved using standard conic optimization packages. In addition, we develop conditions for the optimal precoder for both of these problems, and propose two simple fixed point iterations to find the solutions which
NONSTANDARD DUALITY CONCEPTS IN CONIC AND QUADRATIC OPTIMIZATION
, 2007
"... This thesis is centred around the topic of duality. It presents the classical duality theories in optimization and identifies their key ingredients as convexity and constraint qualification. The thesis answers questions on what we can salvage from the theories if these conditions fail to hold. Fir ..."
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This thesis is centred around the topic of duality. It presents the classical duality theories in optimization and identifies their key ingredients as convexity and constraint qualification. The thesis answers questions on what we can salvage from the theories if these conditions fail to hold
A Conic Formulation for l_pNorm Optimization
, 2000
"... In this paper, we formulate the l p norm optimization problem as a conic optimization problem, derive its standard duality properties and show it can be solved in polynomial time. We first define an ad hoc closed convex cone L p , study its properties and derive its dual. This allows us to express ..."
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Cited by 11 (1 self)
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In this paper, we formulate the l p norm optimization problem as a conic optimization problem, derive its standard duality properties and show it can be solved in polynomial time. We first define an ad hoc closed convex cone L p , study its properties and derive its dual. This allows us to express
Inverse conic programming with applications
, 2005
"... Linear programming duality yields efficient algorithms for solving inverse linear programs. We show that special classes of conic programs admit a similar duality and, as a consequence, establish that the corresponding inverse programs are efficiently solvable. We discuss applications of inverse co ..."
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Cited by 5 (0 self)
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Linear programming duality yields efficient algorithms for solving inverse linear programs. We show that special classes of conic programs admit a similar duality and, as a consequence, establish that the corresponding inverse programs are efficiently solvable. We discuss applications of inverse
Proving Strong Duality for Geometric Optimization Using a Conic Formulation
, 1999
"... Geometric optimization is an important class of problems that has many applications, especially in engineering design. In this article, we provide new simplified proofs for the wellknown associated duality theory, using conic optimization. After introducing suitable convex cones and studying their ..."
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Cited by 8 (1 self)
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Geometric optimization is an important class of problems that has many applications, especially in engineering design. In this article, we provide new simplified proofs for the wellknown associated duality theory, using conic optimization. After introducing suitable convex cones and studying
Inverse Conic Programming And Applications
, 2003
"... The past decade has seen a growing interest in inverse optimization. It has been shown that duality yields very efficient algorithms for solving inverse linear programming problems. In this paper, we consider a special class of conic programs that admits a similar duality and show that the correspon ..."
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The past decade has seen a growing interest in inverse optimization. It has been shown that duality yields very efficient algorithms for solving inverse linear programming problems. In this paper, we consider a special class of conic programs that admits a similar duality and show
Quantizations of conical symplectic resolutions II: category O and symplectic duality
 In preparation
"... We define and study category O for a symplectic resolution, generalizing the ..."
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Cited by 10 (7 self)
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We define and study category O for a symplectic resolution, generalizing the
Results 11  20
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89