Related papers: Calmness modulus of linear semi-infinite programs
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
Absolute value linear programming problems is quite a new area of optimization problems, involving linear functions and absolute values in the description of the model. In this paper, we consider interval uncertainty of the input…
In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and…
We produce approximation bounds on a semidefinite programming relaxation for sparse principal component analysis. These bounds control approximation ratios for tractable statistics in hypothesis testing problems where data points are…
In this paper, we propose a new robust analysis tool motivated by large-scale systems. The H infinity norm of a system measures its robustness by quantifying the worst-case behavior of a system perturbed by a unit-energy disturbance.…
This paper considers the problem of minimizing the ordered weighted average (or ordered median) function of finitely many rational functions over compact semi-algebraic sets. Ordered weighted averages of rational functions are not, in…
A number of recent results on optimization problems involving submodular functions have made use of the multilinear relaxation of the problem. These results hold typically in the value oracle model, where the objective function is…
We characterize the maximum controlled invariant (MCI) set for discrete- as well as continuous-time nonlinear dynamical systems as the solution of an infinite-dimensional linear programming problem. For systems with polynomial dynamics and…
Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of sparse sub-gaussian random projections to approximate…
Monotonicity constraints are powerful regularizers in statistical modelling. They can support fairness in computer-aided decision making and increase plausibility in data-driven scientific models. The seminal min-max (MM) neural network…
A matrix optimization problem over an uncertain linear system on finite horizon (abbreviated as MOPUL) is studied, in which the uncertain transition matrix is regarded as a decision variable. This problem is in general NP-hard. By using the…
Constraint programming uses enumeration and search tree pruning to solve combinatorial optimization problems. In order to speed up this solution process, we investigate the use of semidefinite relaxations within constraint programming. In…
We present an explicit solution to the discrete-time Bellman equation for minimax optimal control of positive systems under unconstrained disturbances. The primary contribution of our result relies on deducing a bound for the disturbance…
The simplex algorithm for linear programming is based on the fact that any local optimum with respect to the polyhedral neighborhood is also a global optimum. We show that a similar result carries over to submodular maximization. In…
Inspired by classical sensitivity results for nonlinear optimization, we derive and discuss new quantitative bounds to characterize the solution map and dual variables of a parametrized nonlinear program. In particular, we derive explicit…
While globally optimal solutions to many convex programs can be computed efficiently in polynomial time, this is, in general, not possible for nonconvex optimization problems. Therefore, locally optimal approaches or other efficient…
Semi-infinite programs are a class of mathematical optimization problems with a finite number of decision variables and infinite constraints. As shown by Blankenship and Falk (Blankenship and Falk. "Infinitely constrained optimization…
In this paper, we leverage an information-theoretic upper bound on the maximum admissible level of noise (MALN) in convex Lipschitz-continuous zeroth-order optimisation to establish corresponding upper bounds for classes of strongly convex…
In this paper, "chance optimization" problems are introduced, where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective…
Semidefinite relaxations of polynomial optimization have become a central tool for addressing the non-convex optimization problems over non-commutative operators that are ubiquitous in quantum information theory and, more in general,…