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We are focusing on bound constrained global optimization problems, whose objective functions are computationally expensive black-box functions and have multiple local minima. The recently popular Metric Stochastic Response Surface (MSRS)…
We study a linear contextual optimization problem where a decision maker has access to historical data and contextual features to learn a cost prediction model aimed at minimizing decision error. We adopt the predict-then-optimize framework…
Significant effort has been made to solve computationally expensive optimization problems in the past two decades, and various optimization methods incorporating surrogates into optimization have been proposed. However, most optimization…
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…
We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…
This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic…
This manuscript proposes a probabilistic framework for algorithms that iteratively solve unconstrained linear problems $Bx = b$ with positive definite $B$ for $x$. The goal is to replace the point estimates returned by existing methods with…
Multiobjective combinatorial optimization deals with problems considering more than one viewpoint or scenario. The problem of aggregating multiple criteria to obtain a globalizing objective function is of special interest when the number of…
We present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems, and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…
Decision makers routinely use constrained optimization technology to plan and operate complex systems like global supply chains or power grids. In this context, practitioners must assess how close a computed solution is to optimality in…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
In this paper, we introduce a framework for solving finite-horizon multistage optimization problems under uncertainty in the presence of auxiliary data. We assume the joint distribution of the uncertain quantities is unknown, but noisy…
In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In…
Motivated by energy management for micro-grids, we study convex optimization problems with uncertainty in the objective function and sequential decision making. To solve these problems, we propose a new framework called ``Online…
We propose a framework for modeling and solving low-rank optimization problems to certifiable optimality. We introduce symmetric projection matrices that satisfy $Y^2=Y$, the matrix analog of binary variables that satisfy $z^2=z$, to model…
This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework formulates these problems as network models, in that enumerating the Pareto frontier…
This paper introduces the notion of upper-linearizable/quadratizable functions, a class that extends concavity and DR-submodularity in various settings, including monotone and non-monotone cases over different convex sets. A general…
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…
A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…