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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…
Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
Coordinate-wise minimization is a simple popular method for large-scale optimization. Unfortunately, for general (non-differentiable) convex problems it may not find global minima. We present a class of linear programs that coordinate-wise…
This paper introduces an efficient algorithm for computing the best approximation of a given matrix onto the intersection of linear equalities, inequalities and the doubly nonnegative cone (the cone of all positive semidefinite matrices…
A core challenge in policy optimization in competitive Markov decision processes is the design of efficient optimization methods with desirable convergence and stability properties. To tackle this, we propose competitive policy optimization…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
We investigate relaxations for a class of discrete bilevel programs where the interaction constraints linking the leader and the follower are linear. Our approach reformulates the upper-level optimality constraints by projecting the…
The problem of optimizing over the cone of nonnegative polynomials is a fundamental problem in computational mathematics, with applications to polynomial optimization, control, machine learning, game theory, and combinatorics, among others.…
Motivated by the expressive power of completely positive programming to encode hard optimization problems, many approximation schemes for the completely positive cone have been proposed and successfully used. Most schemes are based on outer…
The central object of this PhD thesis is known under different names in the fields of computer science and statistical mechanics. In computer science, it is called the Maximum Cut problem, one of the famous twenty-one Karp's original…
We show that $\varepsilon$-additive approximations of the optimal value of fixed-size two-player free games with fixed-dimensional entanglement assistance can be computed in time $\mathrm{poly}(1/\varepsilon)$. This stands in contrast to…
We consider nonlinear model predictive control (MPC) with multiple competing cost functions. In each step of the scheme, a multiobjective optimal control problem with a nonlinear system and terminal conditions is solved. We propose an…
Given a compact parameter set $Y\subset R^p$, we consider polynomial optimization problems $(P_y$) on $R^n$ whose description depends on the parameter $y\inY$. We assume that one can compute all moments of some probability measure $\phi$ on…
We consider the problem of designing incentive-compatible, ex-post individually rational (IR) mechanisms for covering problems in the Bayesian setting, where players' types are drawn from an underlying distribution and may be correlated,…
We investigate the computation of equilibria in extensive-form games where ex ante correlation is possible, focusing on correlated equilibria requiring the least amount of communication between the players and the mediator. Motivated by the…
In computer vision, many problems such as image segmentation, pixel labelling, and scene parsing can be formulated as binary quadratic programs (BQPs). For submodular problems, cuts based methods can be employed to efficiently solve…
Colonel Blotto games with discrete strategy spaces effectively illustrate the intricate nature of multidimensional strategic reasoning. This paper studies the equilibrium set of such games where, in line with prior experimental work, the…
We present a continuous nonlinear optimization model for the Spin Glass Problem (SGP), building on a classical result by Rosenberg (1972), which shows that for a class of multilinear polynomial problems the optimal values of the continuous…
In this paper we solve mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. This work is motivated by the MILPs being able to model problems in multi-agent autonomy, such as task assignment problems…