Some NP-complete problems in quadratic and nonlinear programming
Mathematical Programming: Series A and B
Mathematics of Operations Research
Operations Research
Adjustable robust solutions of uncertain linear programs
Mathematical Programming: Series A and B
Multiattribute Preference Analysis with Performance Targets
Operations Research
Optimal Inequalities in Probability Theory: A Convex Optimization Approach
SIAM Journal on Optimization
Convex Approximations of Chance Constrained Programs
SIAM Journal on Optimization
A Robust Optimization Perspective on Stochastic Programming
Operations Research
A Linear Decision-Based Approximation Approach to Stochastic Programming
Operations Research
Satisficing Measures for Analysis of Risky Positions
Management Science
Operations Research
A Decision-Analytic Approach to Reliability-Based Design Optimization
Operations Research
Distributionally Robust Optimization and Its Tractable Approximations
Operations Research
Robust Optimization Made Easy with ROME
Operations Research
Primal and dual linear decision rules in stochastic and robust optimization
Mathematical Programming: Series A and B
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We propose a class of functions, called multiple objective satisficing MOS criteria, for evaluating the level of compliance of a set of objectives in meeting their targets collectively under uncertainty. The MOS criteria include the joint targets' achievement probability joint success probability criterion as a special case and also extend to situations when the probability distributions are not fully characterized. We focus on a class of MOS criteria that favors diversification, which has the potential to mitigate severe shortfalls in scenarios when any objective fails to achieve its target. Naturally, this class excludes joint success probability. We further propose the shortfall-aware MOS criterion S-MOS, which is inspired by the probability measure and is diversification favoring. We also show how to build tractable approximations of the S-MOS criterion. Because the S-MOS criterion maximization is not a convex optimization problem, we propose improvement algorithms via solving sequences of convex optimization problems. We report encouraging computational results on a blending problem in meeting specification targets even in the absence of full probability distribution description.