Related papers: Cutting planes for signomial programming
This paper introduces a new extragradient-type algorithm for a class of nonconvex-nonconcave minimax problems. It is well-known that finding a local solution for general minimax problems is computationally intractable. This observation has…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local…
Various control schemes rely on a solution of a convex optimization problem involving a particular robust quadratic constraint, which can be reformulated as a linear matrix inequality using the well-known $\mathcal{S}$-lemma. However, the…
We consider the problem of minimizing the sum of a smooth function $h$ with a bounded Hessian, and a nonsmooth function. We assume that the latter function is a composition of a proper closed function $P$ and a surjective linear map $\cal…
Cut generation and lifting are key components for the performance of state-of-the-art mathematical programming solvers. This work proposes a new general cut-and-lift procedure that exploits the combinatorial structure of 0-1 problems via a…
Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of…
Weight optimization of frame structures with continuous cross-section parametrization is a challenging non-convex problem that has traditionally been solved by local optimization techniques. Here, we exploit its inherent semi-algebraic…
Our study is motivated by the solution of Mixed-Integer Non-Linear Programming (MINLP) problems with separable non-convex functions via the Sequential Convex MINLP technique, an iterative method whose main characteristic is that of solving,…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
We propose a proximal approach to deal with a class of convex variational problems involving nonlinear constraints. A large family of constraints, proven to be effective in the solution of inverse problems, can be expressed as the lower…
In this paper we introduce a technique to produce tighter cutting planes for mixed-integer non-linear programs. Usually, a cutting plane is generated to cut off a specific infeasible point. The underlying idea is to use the infeasible point…
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…
In this paper, we consider a class of nonconvex and nonsmooth fractional programming problems, that involve the sum of a convex, possibly nonsmooth function composed with a linear operator and a differentiable, possibly nonconvex function…
We propose a successive generation of cutting inequalities for binary quadratic optimization problems. Multiple cutting inequalities are successively generated for the convex hull of the set of the optimal solutions $\subset \{0, 1\}^n$,…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the…
This paper presents a novel outer approximation algorithm for nonsmooth mixed-integer nonlinear programming (MINLP) problems. The method proceeds by fixing the integer variables and solving the resulting nonlinear convex subproblem. When…
We study nonconvex optimization landscapes for learning overcomplete representations, including learning (i) sparsely used overcomplete dictionaries and (ii) convolutional dictionaries, where these unsupervised learning problems find many…