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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mixed volume of infinite-dimensional convex compact sets II
无限维 凸紧集 混合体积
2023/11/6
Using the results presented in the previous lecture, namely the generalization of the Tsirelson's theorem [2] to mixed volumes, we calculate the mixed volume of the closed convex hulls of the two orth...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mixed volume of infinite-dimensional convex compact sets I
无限维 凸紧集 混合体积
2023/11/6
Let K be a convex compact subset of a separable Hilbert space H. One of the most important geometric characteristics of K is its intrinsic volumes. In the finitedimensionalcase (K ? R^d), the intrinsi...
Analysis of linear systems with saturation using convex optimization
Linear matrix inequality linear system the lyapunov function space area half plan
2015/8/11
We show how linear matrix inequalities (LMI) can be used to perform local stability and performance analysis of linear systems with saturating elements. This leads to conservative information on stabi...
Piecewise-affine state feedback for piecewise-affine slab systems using convex optimization
Piecewise-affine systems State feedback Convex optimization Ellipsoids Lyapunov function
2015/8/10
This paper shows that Lyapunov-based state feedback controller synthesis for piecewise-affine (PWA) slab systems can be cast as an optimization problem subject to a set of linear matrix inequalities (...
Upper bounds on algebraic connectivity via convex optimization
Laplace operator matrix algebra connection Laplacian invariant subset matrix convex function
2015/8/10
The second smallest eigenvalue of the Laplacian matrix L of a graph is called its algebraic connectivity. We describe a method for obtaining an upper bound on the algebraic connectivity of a family of...
Graph implementations for nonsmooth convex programs
Convex optimization nonsmooth optimization disciplined convex pro- gramming optimization modeling languages semidefinite programming second-order cone programming conic optimization nondifferentiable functions.
2015/8/10
We describe graph implementations, a generic method for representing a convex function via its epigraph, described in a disciplined convex programming framework. This simple and natural idea allows a ...
Convex piecewise-linear fitting
Convex optimization Piecewise-linear approximation Data fi tting
2015/8/10
We consider the problem of fitting a convex piecewise-linear function, with some specified form, to given multi-dimensional data. Except for a few special cases, this problem is hard to solve exactly,...
Nonlinear Q-design for convex stochastic control
Nonlinear dynamic controller discrete linear constraint convex function parameters are random
2015/8/7
In this note we describe a version of the Q-design method that can be used to design nonlinear dynamic controllers for a discrete-time linear time-varying plant, with convex cost and constraint functi...
Operation and configuration of a storage portfolio via convex optimization
Convex optimization Predictive control Energy management systems
2015/8/7
We consider a portfolio of storage devices which is used to modify a commodity flow so as to minimize an average cost function. The individual storage devices have different parameters that characteri...
Imputing a convex objective function
Optimization parameter optimization parameter function cost function
2015/8/7
We consider an optimizing process (or parametric optimization problem), i.e., an optimization problem that depends on some parameters. We present a method for imputing or estimating the objective func...
Convex optimization in Julia
Convex programming automati cerification symbolic computation multiple dispatch
2015/8/7
This paper describes Convex.jl, a convex optimization modeling framework in Julia. Convex.jl translates problems from a user-friendly functional language into an abstract syntax tree describing the pr...
A perspective-based convex relaxation for switched-affine optimal control
Switched-affne systems optimal control mixed-integer convex programming hybrid systems disjunctive programming.
2015/8/7
We consider the switched-affine optimal control problem, i.e., the problem of selecting a sequence of affine dynamics from a finite set in order to minimize a sum of convex functions of the system sta...
A semidefinite programming method for integer convex quadratic minimization
The quadratic function the probability of integer zinc, values
2015/8/7
We consider the NP-hard problem of minimizing a convex quadratic function over the integer lattice Zn. We present a semidefinite programming (SDP) method for obtaining a nontrivial lower bound on the ...
On Co-ordinated Quasi-Convex Functions
co-ordinates quasi-convex Wright-quasi-convex Jensen-quasiconvex
2011/2/21
In this paper, we give some definitions on quasi-convex functions and we prove inequalities contain J-quasi-convex and W-quasi-convex functions.We give also some inclusions.
On norm sub-additivity and super-additivity inequalities for concave and convex functions
Matrix Norm Inequality Positive Semidefinite Matrix Convex
2011/1/20
Sub-additive and super-additive inequalities for concave and convex functions have been generalized to the case of matrices by several authors over a period of time.These lead to some interesting ineq...