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On tractable approximations of uncertain linear matrix inequalities affected by interval uncertainty
 SIAM Journal on Optimization
, 2002
"... Abstract. We present efficiently verifiable sufficient conditions for the validity of specific NPhard semiinfinite systems of Linear Matrix Inequalities (LMI’s) arising from LMI’s with uncertain data and demonstrate that these conditions are “tight ” up to an absolute constant factor. In particular ..."
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Abstract. We present efficiently verifiable sufficient conditions for the validity of specific NPhard semiinfinite systems of Linear Matrix Inequalities (LMI’s) arising from LMI’s with uncertain data and demonstrate that these conditions are “tight ” up to an absolute constant factor. In particular, we prove that given an n × n interval matrix Uρ = {A  Aij − A ∗ ij  ≤ ρCij}, one can build a computable lower bound, accurate within the factor π, on the supremum of those ρ for which 2 all instances of Uρ share a common quadratic Lyapunov function. We then obtain a similar result for the problem of Quadratic Lyapunov Stability Synthesis. Finally, we apply our techniques to the problem of maximizing a homogeneous polynomial of degree 3 over the unit cube. Key words. Robust semidefinite optimization, data uncertainty, Lyapunov stability synthesis, relaxations of combinatorial problems AMS subject classifications. 90C05, 90C25, 90C30
Algorithms and Software for LMI Problems in Control
 IEEE Control Systems Magazine
, 1997
"... this article is to provide an overview of the state of the art of ..."
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Cited by 8 (0 self)
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this article is to provide an overview of the state of the art of
Adjustable robust optimization models for nonlinear multiperiod optimization
, 2004
"... We study multiperiod nonlinear optimization problems whose parameters are uncertain. We assume that uncertain parameters are revealed in stages and model them using the adjustable robust optimization approach. For problems with polytopic uncertainty, we show that quasiconvexity of the optimal valu ..."
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Cited by 6 (0 self)
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We study multiperiod nonlinear optimization problems whose parameters are uncertain. We assume that uncertain parameters are revealed in stages and model them using the adjustable robust optimization approach. For problems with polytopic uncertainty, we show that quasiconvexity of the optimal value function of certain subproblems is sufficient for the reducibility of the resulting robust optimization problem to a singlelevel deterministic problem. We relate this sufficient condition to the quasi coneconvexity of the feasible set mapping for adjustable variables and present several examples and applications satisfying these conditions. 1
RECENT DEVELOPMENTS IN FRACTIONAL PROGRAMMING: SINGLE RATIO AND MAXMIN CASE
"... Abstract. We review some recent developments in singleratio and generalized fractional programming. In the latter case we focus on the maximization of the smallest of several ratios. To introduce these newer results, we provide the necessary context by including some major existing results [63]. In ..."
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Abstract. We review some recent developments in singleratio and generalized fractional programming. In the latter case we focus on the maximization of the smallest of several ratios. To introduce these newer results, we provide the necessary context by including some major existing results [63]. In this concise survey we consider applications, theory and algorithms. 1.
PseudoLinear Programming
, 1998
"... This short note revisits an algorithm previously sketched by Mathis and Mathis, Siam Review 1995, and used to solve a nonlinear hospital fee optimization problem. An analysis of the problem structure reveals how the Simplex algorithm, viewed under the correct light, can be the driving force behind a ..."
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Cited by 3 (0 self)
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This short note revisits an algorithm previously sketched by Mathis and Mathis, Siam Review 1995, and used to solve a nonlinear hospital fee optimization problem. An analysis of the problem structure reveals how the Simplex algorithm, viewed under the correct light, can be the driving force behind a successful algorithm for a nonlinear problem. 1 A seemingly nonlinear program In a past Classroom Notes column, [6] Mathis and Mathis introduces an interesting optimization problem. Practical, in this era of budget constraints, their model describes a facet of hospital revenue and is used by managers in Texas to help in decision making. Even more interesting, for the theoretically minded, is the fact that a trivial algorithm seems to solve, albeit without a convergence proof, a nonlinear, arguably difficult problem. We revisit this problem to give a strong mathematical foundation to a slightly modified algorithm and explain, along the way, why the problem is much simpler than expected at f...