Related papers: A Monotonic Optimization Approach for Solving Stri…
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…
In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
This paper proposes a robust approximation method for solving chance constrained optimization (CCO) of polynomials. Assume the CCO is defined with an individual chance constraint that is affine in the decision variables. We construct a…
Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
In this paper we study the fundamental problems of maximizing a continuous non-monotone submodular function over the hypercube, both with and without coordinate-wise concavity. This family of optimization problems has several applications…
We investigate robust optimization problems defined for maximizing convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm…
We present a general-purpose interior-point solver for convex optimization problems with conic constraints. Our method is based on a homogeneous embedding method originally developed for general monotone complementarity problems and more…
This paper deals with approximate solutions of a nonsmooth semi-infinite programming with multiple interval-valued objective functions. We first introduce four types of approximate quasi Pareto solutions of the considered problem by…
We describe an elementary algorithm to build convex inner approximations of nonconvex sets. Both input and output sets are basic semialgebraic sets given as lists of defining multivariate polynomials. Even though no optimality guarantees…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
In this paper, we propose an efficient numerical approach for solving a specific type of quartic inhomogeneous polynomial optimization problem inspired by practical applications. The primary contribution of this work lies in establishing an…
In many practical applications, heuristic or approximation algorithms are used to efficiently solve the task at hand. However their solutions frequently do not satisfy natural monotonicity properties of optimal solutions. In this work we…
Real-world machine learning applications may require functions that are fast-to-evaluate and interpretable. In particular, guaranteed monotonicity of the learned function can be critical to user trust. We propose meeting these goals for…
We propose an algorithm for a family of optimization problems where the objective can be decomposed as a sum of functions with monotonicity properties. The motivating problem is optimization of hyperparameters of machine learning…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…