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The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…
We consider the problem of estimating a low-rank matrix from a noisy observed matrix. Previous work has shown that the optimal method depends crucially on the choice of loss function. In this paper, we use a family of weighted loss…
In this paper, we propose an arc-search infeasible-interior-point algorithm. We show that this algorithm is polynomial and the polynomial bound is ${\cal O}(nL)$ which is at least as good as the best existing bound for…
This work addresses the problem of risk-sensitive control for nonlinear systems with imperfect state observations, extending results for the linear case. In particular, we derive an algorithm that can compute local solutions with…
Autonomous navigation often requires the simultaneous optimization of multiple objectives. The most common approach scalarizes these into a single cost function using a weighted sum, but this method is unable to find all possible trade-offs…
This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…
The problems of determining the optimal power allocation, within maximum power bounds, to (i) maximize the minimum Shannon capacity, and (ii) minimize the weighted latency are considered. In the first case, the global optima can be achieved…
We consider a decision network on an undirected graph in which each node corresponds to a decision variable, and each node and edge of the graph is associated with a reward function whose value depends only on the variables of the…
In this short note, we discuss a goal-oriented multiobjective optimization problem for system performance assessment. The objective function for such optimization problem, which is usually a composite of different performance indices…
In this paper, we develop an online optimization algorithm for solving a class of nonconvex optimization problems with a linearly varying optimal point. The global convergence of the algorithm is guaranteed using the circle criterion for…
This paper is concerned with linear parameter-dependent systems and considers the notion uniform ensemble reachability. The focus of this work is on constructive methods to compute suitable parameter-independent open-loop inputs for such…
We analyze combinatorial optimization problems with ordinal, i.e., non-additive, objective functions that assign categories (like good, medium and bad) rather than cost coefficients to the elements of feasible solutions. We review different…
We look at the number of solutions of an equation of the form f_1*f_2*...*f_k=a in a finite field, where each f_i is a multilinear polynomial. We use two methods to construct a solution of this problem for the cases a=0, a<>0, and we…
We prove that unless P=NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can test whether the optimal value of a nonlinear optimization problem where the objective and constraints are given by low-degree…
Multi-variable nonlinear fuzzy optimization problem is considered under linear order relation on fuzzy numbers. Using gH-differentiability of a fuzzy-valued function $\tilde{f}$, new necessary and sufficient optimality conditions are…
In this work, we study the problem of finding the maximum value of a non-negative submodular function subject to a limit on the number of items selected, a ubiquitous problem that appears in many applications, such as data summarization and…
This work studies and develop projection-free algorithms for online learning with linear optimization oracles (a.k.a. Frank-Wolfe) for handling the constraint set. More precisely, this work (i) provides an improved (optimized) variant of an…
In this paper we propose a (non-linear) smoothing algorithm for group-affine observation systems, a recently introduced class of estimation problems on Lie groups that bear a particular structure. As most non-linear smoothing methods, the…
We consider the problem of discounted optimal state-feedback regulation for general unknown deterministic discrete-time systems. It is well known that open-loop instability of systems, non-quadratic cost functions and complex nonlinear…
In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local…